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Evaluation of the effects of bolus air gaps on surface dose in radiation therapy and possible clinical… Shaw, Adam 2018

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Evaluation of the Effects of Bolus Air Gaps on Surface Dose inRadiation Therapy and Possible Clinical ImplicationsbyAdam ShawM.Sc., University of Oxford, 2009A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Physics)The University of British Columbia(Vancouver)August 2018c© Adam Shaw, 2018The following individuals certify that they have read, and recommend to the Faculty of Graduateand Postdoctoral Studies for acceptance, the thesis entitled:Evaluation of the Effects of Bolus Air Gaps on Surface Dose in Radiation Therapyand Possible Clinical Implicationssubmitted by Adam Shaw in partial fulfillment of the requirements for the degree of Master ofScience in Physics.Examining Committee:Cheryl Duzenli, Physics and AstronomySupervisorBradford Gill, BC Cancer AgencySupervisory Committee MemberiiAbstractIn clinical radiotherapy, treatments are frequently delivered using photons with energies in theMegavoltage range. The advantage of such beam energies is that the majority of dose is depositeddeeper within the patient, with the depth of maximum dose being up to several centimetres beyondthe patient’s skin. This effect allows radiotherapists to target tumours on organs such as the prostate.However, there are times when larger doses must be deposited to the near-skin region. In thesecases, a layer of ”substitute tissue” called a bolus is applied, to shift dose towards the patient’sskin. Given the natural contours of the human body, it is difficult for a bolus to achieve perfectcontact with the patient and air gaps are often present between the applied bolus and the patient’ssurface. Such air gaps have the potential to disturb the distribution of surface dose. In this thesiswe present an investigation into the magnitude of the effects of bolus-surface air gaps on 6 MVphoton beam surface dose.Using a combination of ionization chamber measurements, film dosimetry, and Monte Carlosimulations, we establish that surface dose is significantly reduced in the presence of an air gap. Theobserved reduction in dose increases as the distance between the bolus material and the phantomsurface increases, and is more severe at smaller field sizes.By examining simulated and experimentally measured surface-dose-profiles, we demonstratethat bolus-surface gaps alter the shape of the dose distribution near the field boundary. We find thatsurface dose is reduced near the inside of the field edge, with a corresponding increase in dose iniiithe region outside of the defined field. We propose that this effect is caused by low-energy electronsthat are generated within the bolus material, near the field edges, but are then scattered outside ofthe treatment region when passing through the air gap. As such we would recommend that care betaken to reduce the size of any air gaps to below 1 cm, especially in cases with weaker treatmentbeams and where the PTV is located near to at-risk organs.ivLay SummaryThe use of X-rays to treat cancer requires precise control over the amount of radiation dose de-livered by the treatment beam. Most clinical X-rays are in the Megavoltage energy range, whichallows radiation to penetrate deeper into tissue and deliver the majority of dose up to several cen-timetres beyond the patient’s skin. This allows the treatment of internal organs but is not suitableto address tumours closer to the skin. In such cases, radiotherapists may apply a layer of artificialtissue upon the body. The energy is allowed to build-up within this layer so the maximum the doseis delivered closer to the patient’s skin. However, the presence of air gaps between the skin surfaceand this layer of “bolus” material can effect the distribution of dose. In this thesis, we present aninvestigation into the effects of such air gaps and discuss possible implications for radiotherapytreatments.vPrefaceThis dissertation is original and independent work by the author, Adam Shaw. None of the text ofthe dissertation is taken directly from previously published or collaborative articles.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAbbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction to Radiotherapy Physics . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Interactions of Radiation in Matter . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Dose, Kerma and Electronic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 51.4 The Clinical Application of Bolus . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 The Effect of Bolus-skin Gaps on Surface Dose . . . . . . . . . . . . . . . . . . . 112 Experimental and Simulated Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . 162.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Experimental Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.1 Ionization Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18vii2.2.2 Parallel-Plate Ionization Chambers . . . . . . . . . . . . . . . . . . . . . . 212.2.3 Radiochromic Film Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . 242.2.4 Factors Effecting Dose Response in Film . . . . . . . . . . . . . . . . . . 252.2.5 Films for Surface Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . 272.3 Computer Simulated Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.3.1 The Analytical Anisotropic Algorithm . . . . . . . . . . . . . . . . . . . . 312.3.2 The Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.3.3 Monte Carlo for Surface Dose Calculation . . . . . . . . . . . . . . . . . . 392.3.4 Comparison of Dose Calculation Algorithms Regarding Surface Dose . . . 423 Validation of Monte Carlo Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.2 The Design of Virtual Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3 Interfacing DOSXYZnrc and Eclipse . . . . . . . . . . . . . . . . . . . . . . . . . 533.4 Monte Carlo Simulations and Analysis. . . . . . . . . . . . . . . . . . . . . . . . 553.5 Experimental Validation of Simulated PDD Curves . . . . . . . . . . . . . . . . . 583.6 Results of the Validation Experiments . . . . . . . . . . . . . . . . . . . . . . . . 644 The Effects of Bolus-Skin Gaps on Surface Dose . . . . . . . . . . . . . . . . . . . . 714.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.2 Measuring and Analysing Surface Dose Effects . . . . . . . . . . . . . . . . . . . 724.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 The Effects of Bolus-Skin Gaps on Lateral Dose Profiles . . . . . . . . . . . . . . . . 845.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856 Conclusions and Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956.2 Suggested Future Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100A Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105A.1 getPDD.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105A.2 getDsurf.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109viiiA.3 Yprofs.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111ixList of TablesTable 5.1 Coefficents obtained from fitting a Logistic function to the shape of lateral doseprofiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Table 5.2 Values showing the dependence of profile penumbra on the size of bolus-surfaceair gaps. Experimental values were obtained directly from EBT 3 measure-ments. Values were estimated from Monte Carlo (MC) results using logisticregression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90xList of FiguresFigure 1.1 Plot showing the relationship between the probability of a photon undergoingone of the four specified interaction events in water, as quantified by the massattenuation coefficient, and its energy. The solid black line represents the totalmass attenuation coefficient µ/ρ , defined as the sum of the separate attenuationcoefficients of each interaction. This figure was constructed using data freelyavailable from NIST. [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Figure 1.2 A schematic illustration showing the formation of electron equilibrium. Thegrid represents the medium, with letters A-F indicating regions of increasingdepth. Red arrows indicate photons, which in turn, set electrons into motion.The blue arrows indicate the paths of multiple electrons and the majority oftheir energy are deposited towards the end of their tracks (green stars). . . . . 7Figure 1.3 Percent depth dose curve of a 6 MV beam in water, as simulated using theEclipse treatment planning system. Field size of the beam was 10x10 cm2.Region A indicates the ”build-up” region demonstrating a rapid increase indose near the surface. In Region B is the dose gradually decreases with depthdue to attenuation. zm represents the depth of dose maximum, which for a 6MV beam in water is approximately 1.5 cm . . . . . . . . . . . . . . . . . . . 9xiFigure 1.4 A schematic illustrating how bolus can be used to achieve more efficient de-position of dose into the Planning Target Volume (PTV). The maximum doseshould, ideally, be deposited in the centre of the PTV at depth zc (Point A).Without the use of bolus, the dose will be distributed according to the red PDDcurve. In this case, it is clear that the maximum dose will miss the PTV and willinstead coincide with point B. However, if water-equivalent bolus of thicknesst (blue rectangle) is added to the surface, the PDD will be shifted as shown bythe blue curve. Now the depth of maximum dose will coincide with point A,as desired. The thickness t can be determined as t = zm− zc . . . . . . . . . . 15Figure 2.1 A simplified schematic showing the key design features of a Fixed SeparationParallel Plate Ionization Chamber. . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 2.2 A schematic illustrating how mass attenuation data can be mapped into a prob-ability in the range [0,1]. MC algorithms use a randomly generated number R,whose place in this range is used to determine the interaction of a simulatedphoton. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 3.1 Schematic showing the apparatus used for our Monte Carlo simulations. Thephase space source corresponds to the source of the virtual 6 MV linac. Note,that the origin of the system is defined at the centre of the phantom’s surface.The bolus floats in air above the phantom within the negative -z region. Ourmeasurement points are within the phantom body i.e. the +z region. Surfacedose is measured at Dsurf, which is located in the centre of the voxels immedi-ately below the origin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 3.2 Schematic showing the voxel distribution for the virtual phantom used in ourMC simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52xiiFigure 3.3 Flow chart illustrating the process used to create MC simulations from EclipseTreatment Planning System - Developed by Varian Medical Systems (ECLIPSETM)treatment plans using idealized virtual phantoms. Rectangular boxes representprocesses and parallelograms indicate output files that would be fed into othersubsequent steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 3.4 The experimental geometry for Percentage Depth Dose (PDD) measurementswith a Markus parallel-plate ionization chamber . . . . . . . . . . . . . . . . . 59Figure 3.5 The experimental geometry for PDD measurements with EBT3 radiochromicfilms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 3.6 Comparison of PDD curves, obtained using a Markus parallel plate chamber,EBT3 films, MC, andAnalytical Anisotropic Algorithm (AAA) for 5x5, 10x10and 15x15 cm2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 3.7 Comparison of the build-up region for PDD curves, obtained using a Markusparallel plate chamber, EBT3 films, MC, and AAA for all field sizes. . . . . . . 70Figure 4.1 Experimental procedure for measurement of surface dose with increasing gapsize, using a Markus parallel plate chamber (a) and EBT3 film (b). c) A pho-tograph showing the phantom and bolus assembled for use in Markus chamberexperiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 4.2 MC results showing effect of bolus-surface gaps (g) on surface dose. Dosesare given normalised by the surface dose measured when no air gap is present(g = 0). Absolute errors in relative dose (∆) are two small to be shown andwere less than 0.006 for all field sizes. Bolus thickness was 1 cm. . . . . . . . 77Figure 4.3 The effect of bolus-surface gaps on surface dose for a 10x10 cm2 field asmeasured using MC, AAA, EBT3 films and a Markus parallel-plate ionizationchamber. Bolus thickness = 1 cm . . . . . . . . . . . . . . . . . . . . . . . . . 78xiiiFigure 4.4 The effect of bolus-surface gap size on PDD (each curve is normalized to itsown maximum dose), as shown for the first 5 cm. It can be seen that thepresence of large gaps restores the build-up of dose near to the surface, inagreement with the results of Sroka et.al [44]. Bolus thickness = 1 cm . . . . . 80Figure 5.1 Variation in the shape of the lateral surface dose distribution due to increasingbolus-surface distance. Each profile presents the dose relative to the mean doseat the centre of the field (Ξ(x,g)). Data was derived from a) Monte Carlo andb) EBT3 film measurements. Bolus thickness = 1 cm. . . . . . . . . . . . . . 87Figure 5.2 Monte Carlo calculated relative dose profiles for the edge of a 6 MV beam with10x10 cm2 field. The data points are fitted with the logistic function defined inEquation 5.2 (solid lines). Bolus thickness = 1 cm . . . . . . . . . . . . . . . 88Figure 5.3 a) Lateral dose profiles for a 10x10 cm 2 at different depths. For comparisonthe black line represents the relative dose at the surface for g =0. b) Decreaseof fractional penumbra (ratio of measured penumbra to corresponding value atg = 0) with depth. Bolus thickness = 1 cm . . . . . . . . . . . . . . . . . . . 92xivAbbreviationsIMRT Intensity Modulated RadiotherapyTPS Treatment Planning SystemPDD Percentage Depth DoseMC Monte CarloAAA Analytical Anisotropic AlgorithmVMAT Volumetric Modulated Arc TherapyBCCA BC Cancer AgencyMLC Multi-leaf collimatorQA Quality AssurancePTV Planning Target VolumeCTV Clinical Target VolumeECLIPSETM Eclipse Treatment Planning System - Developed by Varian Medical SystemsTLD Thermoluminescent DosimeterDRF Dose Reduction FactorPP Parallel-platexvAcknowledgmentsThe work of study and research that has gone into producing this thesis would never have beencompleted without the support of many dear friends and colleagues.First, I would like to thank my family of all they have done for me: Ashley, my dear wife, forher continual love and support, and James, my tiny man, for being a constant source of joy andinspiration. Also, thank you to my beagles, Bucky and Harley, for not eating my thesis.Thank you to my supervisors, Cheryl Duzenli and Brad Gill, for the immense patience andhelpful advice that has made this work possible. I would also like to thank all of my colleagues inthe Department of Medical Physics and the BC Cancer Agency; especially Dr Tony Popescu andParmveer Atwal, for helping to get me started with the Monte Carlo simulations, and Joel Beaudryfor his assistance with the experiments.Finally, I want to express how much I have valued the opportunity to work at the BC CancerAgency. The importance of the work done by the BCCA cannot possibly be overstated and I amvery proud to have contributed, if in a small way, to that great work.xviChapter 1Introduction to Radiotherapy Physics1.1 IntroductionIn clinical radiotherapy, a primary role of the physicist is to ensure that a patient receives the correctquantity of radiation (i.e. dose) to the target volume, as prescribed by the radiation oncologist. Toperform this task, physicists must understand the many factors that affect how radiation spreadsthrough, and is absorbed by, living tissue. Many of the fundamental mechanisms underpinningthese processes are well-understood. However, modern radiotherapy offers many options withregards to patient set-up, beam geometry and the modification of beam properties. The effect thesevarious factors have on patient dose have to be carefully studied and quantified to ensure safe andaccurate treatment planning and delivery.In the work described in this thesis, we shall focus on challenges regarding the application ofbolus in modern radiotherapy. Further discussion of the physics that necessitates the use of bolusin clinical situations shall follow later in this chapter. In brief, the term bolus is used to refer to anymaterial that is placed on the patient’s skin as a form of “artificial tissue”. Current radiotherapytreatments primarily use beam energies in the Megavoltage (MV) range. At these energies themaximum dose is deposited deeper in the tissues, to allow treatment of internal structures such1as lungs and the prostate. However, it is often necessary to treat structures closer to the skin.By adding a layer of additional “tissue” through which the beam must penetrate, the region ofmaximum dose deposition is effectively shifted towards the surface. However, given the contoursof the human body and possible interference from treatment apparatus (e.g. patient immobilizingmasks) it is often not possible to place the bolus in full contact with the skin, leading to the presenceof gaps between bolus and patient. The aim of this research project has been to elucidate the effectthat these gaps have on the distribution of surface dose.To set this question into its full context, it is first necessary to understand the effects that radia-tion has on tissue and how they may be meaningfully quantified and measured, i.e. it is necessaryto understand what is meant by dose.1.2 Interactions of Radiation in MatterThe term radiation refers to the propagation of energy through a medium via the action of someform of particles. These particles can be charged (e.g. protons), uncharged (neutrons), or evenmassless (photons). In this work we shall be concerned with the behaviour of X-rays, which arestreams of high-energy photons, and are the most commonly used form of radiation in clinicalpractise.As photons pass through matter they interact with the atoms through absorption or scatteringprocesses, as listed below. It is impossible to predict which particular photon will undergo whichinteraction, rather, only the relative probabilities of these events can be discussed. The probabilityof each interaction is determined by its attenuation coefficient µ , which represents the probabil-ity that a photon will experience a specified interaction per until length travelled in the medium[26] [29]. As the probability of a photon interacting with the medium’s atoms will depend onhow closely they are packed (i.e. their density), a more useful quantity is the mass attenuationcoefficient, which is simply the attenuation coefficient divided by the density µ/ρ .2Another key factor influencing the probability that an incident photon undergoes a given in-teraction, rather than some other process, is its energy. Scattering events can loosely be describedas collisions between incident photons and the electrons of an atom. It is the energy of the pho-ton, relative to the binding energy of the electron, that determines whether the photon is“strong”enough to transfer sufficient energy to knock out the electron (Compton scattering) or if the pho-ton rebounds elastically, retaining all of its initial kinetic energy but travelling in a new direction(Rayleigh Scattering) [29]. In absorption events, the photon’s energy has to be equal or higherthan some threshold value, either the binding energy (photoelectric effect) or the rest mass of anelectron-position pair (pair production) for the event to occur at all. Figure 1.1 shows the relation-ship between the mass attenuation coefficient and the incident energy for photons propagating inwater.Rayleigh Scattering In this process, the incident photon is deflected by the bound electrons thatsurround the nucleus. This primarily occurs when the energy of the incoming photon is verysmall compared to the binding energy of the atom’s electrons, and simply “bounces off”.As there is no transfer of energy from the photon to the medium, this interaction does notcontribute to dose.Compton Scattering When the energy of the incident photon is much higher than the bindingenergies of the atom’s electrons, the electron can be approximately considered as unboundor “free”. When the photon “collides” with the electron it transfers some of its energy andmomentum and the electron is sent travelling through the medium. The photon also continuesto propagate, albeit in a new direction, having lost some energy, and can undergo furtherinteraction events.Photoelectric Emission At energies comparable to the binding energy of the medium, the photoncan be absorbed, transferring all of its energy to ionize an electron in the atom’s core shells.3Figure 1.1: Plot showing the relationship between the probability of a photon undergoing oneof the four specified interaction events in water, as quantified by the mass attenuationcoefficient, and its energy. The solid black line represents the total mass attenuationcoefficient µ/ρ , defined as the sum of the separate attenuation coefficients of each in-teraction. This figure was constructed using data freely available from NIST. [1]Much of the original photon energy is used in unbinding the core electron, however, anyadditional energy is turned to kinetic energy so the newly free electron is emitted into themedium.Pair/Triplet Production At high enough energies the photon can interact with the strong electricfield surrounding the atomic nucleus, triggering the spontaneous decay of the photon into two4charged particles, an electron and a positron (an anti-electron). As with the photoelectriceffect, this absorption process can only occur if the incident photon has energy above acertain threshold. In this case, that threshold is 1.022 MeV, which is the energy necessary toconstitute the rest-mass of both electron and positron. Above this threshold, the additionalphoton energy is given to the newly formed particles as kinetic energy.With the exception of Rayleigh scattering, in each of the four processes described above, trans-fer of energy from incident photons causes the release of energetic electrons into the medium. Un-like photons, electrons deposit energy into the medium through a continuous series of successiveinteractions with the electric fields that surround atoms. Some of these interactions can produceadditional photons (Bremsstrahlung), however, most are simple collisional processes. The energydeposited by the electron, per unit distance, is quantified by the stopping power S. As with theattenuation coefficient for photons, this quantity is often normalized by the medium’s density andthis quantity is called the mass stopping power.Sρ=1ρdEdx(1.1)The majority of the energy lost through electron collisions is dissipated as heat [29]. However,some fraction of this energy may trigger radiochemical changes in the medium, such as ionizationof atoms and the formation of free radicals. In living tissue, such biochemical alteration of theDNA can potentially prohibit the reproduction of cells and lead to the death of the tissue. It is inthis way, that radiation can be used to destroy cancer cells.1.3 Dose, Kerma and Electronic EquilibriumAs described in the previous section, the deposition of energy to a medium from X-ray radiation isa process that occurs in two steps:5• Photons transfer kinetic energy to electrons via instantaneous Compton, Pair-production andPhotoelectric interactions.• These electrons deposit energy through successive collisional interactions as they travelthrough the medium. This energy is absorbed by the medium leading to the desired clin-ical effect.To quantify the energies involved, separately, in each of these steps, two quantities are used:Kerma and Dose.[26]Kerma, or Kinetic Energy Released in Medium, represents the energy transferred to electronsby photon interactions. Dose describes the energy that is actually absorbed by the medium. Bothquantities are defined in dimensions of energy/mass, the standard unit of measurement in called theGray: 1Gy = 1J/kg.One key distinction between these closely related concepts, is that the transfer of kerma islocalized where the photon interaction occurred. Dose is deposited into the material more graduallyas electrons pass through. The distribution of dose, therefore, is dependent on the fluence andrange of the electrons released. As the photon beam enters the medium, interactions will occur thatwill trigger the release of electrons from that location. Those electrons will still be propagatingthrough the medium even as the photons travel deeper and send out even more electrons. Newlyliberated electrons join existing electrons as they stream through the material depositing dose, andso on, creating growing cascade of electrons and rapid build-up of dose. Figure 1.2 illustrates thisprocess.In Figure 1.2, photons (red arrows) penetrate the medium, undergoing interactions and trig-gering streams of electrons (blue arrows). For illustrative purposes, the majority of the electronsenergies are deposited into the material at the end of their tracks, as shown by the green stars. Inthe near-surface region (boxes A and B), electrons are released but little energy is absorbed by themedium and so less dose is deposited into this region. Dose gradually builds up as photons pass6deeper into the medium. Starting from box C, at a depth exceeding the mean range of the electrons,the release of electrons becomes coincident with the deposition of the large amounts of dose. Atthis point, the transfer of kerma and the deposition of dose can be considered in equilibrium, a statereferred to as electronic equilibrium.Figure 1.2: A schematic illustration showing the formation of electron equilibrium. The gridrepresents the medium, with letters A-F indicating regions of increasing depth. Redarrows indicate photons, which in turn, set electrons into motion. The blue arrowsindicate the paths of multiple electrons and the majority of their energy are depositedtowards the end of their tracks (green stars).Dose rapidly builds in the material until a quasi-equilibrium is reached between the transferof kinetic energy to electrons and the absorption of energy by the medium. However, the dosedoes not remain constant as the beam is still being attenuated as it passes into the material. There-fore, the number of photons present at greater depths is reduced, as is the transfer of kerma and,consequently, the deposition of dose decreases.The distribution of dose as a function of depth D(z) is well characterised by the Percent DepthDose P, defined below, where D(zm) = Dm represents the maximum dose value, which occurs at adepth of zm.P(z) =D(z)D(zm)×100% (1.2)An example of a Percent Depth Dose (PDD) profile for a 6 MV beam, with a field size of 10 cmx 10 cm, is shown in Figure 1.3. The curve can be described in two regions: a build-up region near7the surface where the dose builds rapidly until electronic equilibrium is reached and an equilibriumregion where dose decreases steadily with depth due to beam attenuation.The value of zm increases at higher photon beam energies. Build-up regions are pronouncedin beams of the megavoltage range, but not at lower energy ranges. This is because photons inthe kilovoltage range, which primarily undergo photoelectric interactions, transfer less kerma tothe electrons in the material and so these electrons do not travel very far. Consequently, dose isdeposited into the material much closer to the site of the photon interactions. It can also be noted,from Figure 1.1, that the attenuation coefficient for kilovoltage photons is much higher than in theMV range and so more photon interaction events can be expected in the near-surface region.As will be discussed in greater detail in Chapter 2, the presence of a high dose-gradient inthe build-up region presents several challenges for the accurate measurement of surface and near-surface dose.1.4 The Clinical Application of BolusIn the previous section, it was shown that a beam of ionising radiation does not deposit dose evenlyas it penetrates deeper into tissue. Instead, the maximum dose is deposited up to several centimetresfrom the surface at the depth of maximum dose (zm). This is a great advantage in most clinicalsituations as this skin-sparing effect allows effective treatment of cancer located deep within thebody.However, it is often necessary to treat tumours close to, or on, the skin surface. This is partic-ularly relevant in cancers of the head and neck and breast regions. In these cases, the skin-sparingeffect is detrimental to the efficient delivery of dose using standard therapeutic photon beams. Theskin-sparing effect can be compensated for by applying layers of tissue-equivalent material (i.e.bolus) to the patient’s skin. The addition of bolus effectively shifts the PDD curve so that the build-8Figure 1.3: Percent depth dose curve of a 6 MV beam in water, as simulated using the Eclipsetreatment planning system. Field size of the beam was 10x10 cm2. Region A indicatesthe ”build-up” region demonstrating a rapid increase in dose near the surface. In RegionB is the dose gradually decreases with depth due to attenuation. zm represents the depthof dose maximum, which for a 6 MV beam in water is approximately 1.5 cmup region occurs within the additional material and the depth of maximum dose coincides with thedesired clinical target. This concept is illustrated in Figure 1.4.To be ideally suited to clinical applications, a bolus material should exhibit the following prop-erties:• Tissue-equivalence9• Malleability - allowing the bolus to conform to patient contours• Reproducibility - to allow bolus characteristics to be maintained over many treatment frac-tions• Non-toxic• Cost-effectiveThe use of bolus is well-established and has a long history within clinical practise. In theircomprehensive review of bolus materials, Vyas et.al[48], cited a report concerning the use of bolusdating to 1920. Although many different materials have been tried, ranging from rice and Play-Dohto speciality products such as SuperflabTM, the essential principle of adding a layer of medium onthe skin to modify the dose distribution has hardly changed. It is very interesting to contrast thisfact with the rapid evolution of treatment delivery in radiotherapy, even within the last few decades.From the introduction of multi-leaf collimators and inverse planning algorithms, to the delivery ofhigh doses using increasingly smaller fields, the ability to sculpt dose distributions to match targetvolumes has seen dramatic progress. These techniques have significantly raised the standard foraccuracy and precision in the calculation and delivery of planned dose distributions.Interesting and clinically relevant questions present themselves when one considers the inter-face of modern treatment delivery and the comparatively “primitive” use of bolus. One exampleis found in a 2002 clinical report by Lee et.al[32]. For precise delivery of the treatment dose totarget volumes, techniques such as Intensity Modulated Radiotherapy (IMRT) need to completelyimmobilise the patient during the course of treatment. A common method to achieve this is toplace a rigid shell over the head, neck, and shoulders. This mask, shaped from thermoplast tocustom fit each individual patient, is fixed to the treatment bed thus preventing movement. Leeand her colleagues observed an increase in adverse skin reactions among their patients who wereimmobilised in this way during IMRT treatments of head-and-neck carcinoma. To find the cause10of this skin toxicity, Lee measured the dose delivered during an IMRT treatment of the neck usingan anthropomorphic phantom. Among their findings was an observed increase in skin-dose of, onaverage, 18% for plans carried out with the immobilisation mask compared to treatments withoutthe mask. The authors attribute this increase in dose to an unforeseen “bolus effect” caused by thepresence of the mask, which led to an increase in dose at the patient’s skin, particularly in regionswhere the thermoplast was at its thickest.Given the rigorous requirements for patient set-up required by modern radiotherapy techniques,the practical constraints of placing a bolus onto a patient, and the limited ability for any material toaccurately conform to the contours of all patients in all treatment sites, it is not difficult to anticipatethe presence of defects. Even minor differences in the thickness of the bolus, or the presence of“small” gaps between the bolus and the patient’s skin may alter the shape and intensity of treatmentdose distribution. Although the scale of these effects may once have been considered small, thehigh precision demanded by modern radiotherapy makes it clinically important to understand thelimitations of commonly used algorithms in accounting for the consequences of bolus in clinicalcontexts.1.5 The Effect of Bolus-skin Gaps on Surface DoseThe central focus of this dissertation is to elucidate the effects that air gaps, occurring between anapplied bolus and the patient’s skin, will have on the magnitude and distribution of surface doseduring treatment with megavoltage photon beams. As such, it is worth presenting a brief sum-mary of the previous literature pertaining to this issue. At time of this writing, three experimentalinvestigations that directly address this question have been reported[13, 30, 44].Despite the expected methodological differences in apparatus used and in the analysis of data,these studies have all come to some consensus regarding the general effects of bolus-skin gaps. Allreports indicate that the surface dose is lower when a gap is present compared to the value recorded11when the bolus is in full-contact with the phantom.These papers also agreed that the magnitude ofthe difference depended on several factors, specifically; field size, beam energy, and the size of theair gap. Each paper found the greatest reduction in surface dose to occur for small field sizes, lowerenergies and large gap sizes.To go into further details, consider the earliest of these investigations published by Butson et.alin 2000 [13]. For a 6 MV beam, 8 x 8 cm2 field, the PDD at the surface was by 2% lower withthe presence of 4 mm gap, compared to when the bolus was in contact with the phantom. Thisdifference in PDD increased to 6% when then gap size was widened to 10 mm. However, with afield size of 10 cm x 20 cm, the change in surface PDD was only 1% and 2% for 4 mm and 10 mmgaps, respectively.Butson’s work is unique among the three studies as it also includes measurements of the influ-ence of bolus air gaps on surface PDDs at oblique beam incidence. At larger beam angles, relativeto normal incidence, the reduction in PDD caused by the presence of an air gap was found to in-crease; up to 10% at 60◦, for 10 mm gaps and a 8x8 cm2 fields. It should also be noted that Butsonet.al did not report any significant differences in surface PDD doses occurring in the presence of2mm air gaps. They also found negligible differences in effect between using a wax or a medi-tekbolus material.One critique of Butson’s methodology is that he analysed the effects of the air gaps by calcu-lating the difference between the surface PDD with and without the presence of the air gap. Aseach PDD for each scenario is, by definition, normalized to the its own maximum dose there isno common point to compare different situations. For example, although the surface PDD for a60◦ beam is 10% lower with a 10 mm gap than the case for the same beam angle without the gap,it is generally the case that PDD values are higher at oblique incidence than at normal incidence.Therefore, from this analysis, it is hard to say if the surface dose at 60◦ with an air gap is, in fact,any lower than at normal incidence with the same air gap.12In their 2010 study, Sroka et.al [44], attempted to look further than the simple issue of surfacedose and instead investigated the effect bolus-skin gaps had on the build-up region of PDD curvesfor 6 MV and 15 MV photon beams. To perform this experiment they used a water tank rather thana solid-water phantom, which allowed for the dosimeter (a parallel plate ionization chamber) to beautomatically scanned, step-wise, along the central beam axis and directly measure the dose curvesat 1 mm resolution.The chief purpose of a bolus is to nullify the skin-sparing effect of megavoltage photon beam.However, Sroka’s results indicate that large bolus-skin gaps reintroduce dose build-up regions. Inthe presence of an air gap, PDD is once again observed to increase with depth and reaches 100%at a new value of zm. Their data shows that this value of zm increases as their air gap widens until,for very large bolus-skin distances, the value of zm is restored to that of an open beam.Sroka attempted to quantify the restoration of the dose build-up region by examining the de-pendence of observed depth of dose maximum zm on the bolus-surface distance g. An empiricalformula, describing a simple exponential relation between the two variables, was fitted to the data.However, ab initio justification of this relationship was offered. Sroka considered the presenceof the bolus to be rendered negligible once air gap was large enough that zm was restored to thestandard value. As an example, for a 6 MV beam and 10 cm x 10 cm field, the value of zm reached1.5 cm for gap sizes larger than 10 cm. For 15 MV beams (same field size) the critical value ofg increased to 25 cm. It should be noted that these air gaps are considerably larger than any thatwould be encountered in any practical medical treatment.In 2013, Yousaf Khan [30], and his colleagues, published the results of a series of aimed atdetermining the effect of bolus-surface gaps on surface dose. This study was the first and, at thetime of this writing, only study to expand its purview beyond simple open beams by measuring theeffect of air gaps on doses delivered by the IMRT technique.13Their initial experiments, using open beam at normal incidence, agree with the general resultsdescribed above i.e. decreasing surface dose corresponding to increasing bolus-surface gaps. Aswith Butson’s findings, Khan’s data shows that the magnitude of the dose reduction was found todepend on field size, with smaller fields exhibiting the largest change and the effects becomingnegligible for fields larger than 15 cm x 15 cm.Khan et.al followed this simple series of experiments by measuring the surface dose delivered toa RANDO anthropomorphic phantom during two clinically-relevant treatment plans. The first wasa 5-field IMRT plan to treat the head and neck, the other was 3D-conformal treatment for the rectumusing the 4-field box technique. Both plans were created using the Eclipse Treatment PlanningSystem - Developed by Varian Medical Systems (ECLIPSETM) and each plan explicitly includedthe shape and location of a custom bolus. Measurements were performed using Gafchromic film.Khan’s results were similar for both plans, with a 1 cm air gap reducing the surface dose by 4-6%,and a 5 cm gap resulting in a 15-25% loss, relative to the dose with no air gap.This last point is key, as modern dosimetry is increasingly becoming a more computationalscience. Algorithmic dose calculations are vital component in both treatment planning and post-treatment quality assurance. Although the effect of a bolus air gap on surface dose has been broadlydescribed by the experiments described above, to our knowledge, no attempt has been made tostudy this specific phenomenon using computational methods. Therefore, a comparison of experi-mental and simulated data regarding the effects of air gaps in bolus is value to the medical physicscommunity, and it is here that have aimed our investigation.14Figure 1.4: A schematic illustrating how bolus can be used to achieve more efficient deposi-tion of dose into the Planning Target Volume (PTV). The maximum dose should, ideally,be deposited in the centre of the PTV at depth zc (Point A). Without the use of bolus,the dose will be distributed according to the red PDD curve. In this case, it is clearthat the maximum dose will miss the PTV and will instead coincide with point B. How-ever, if water-equivalent bolus of thickness t (blue rectangle) is added to the surface, thePDD will be shifted as shown by the blue curve. Now the depth of maximum dose willcoincide with point A, as desired. The thickness t can be determined as t = zm− zc15Chapter 2Experimental and Simulated Dosimetry2.1 IntroductionOne of the key challenges facing the clinical medical physicist is the accurate and reliable mea-surement of radiation dose. As we discussed in the previous chapter, the term “dose” quantifies theeventual absorption of energy into tissue after a series of successive interaction events. Given thevarious ways that the original energy is spread, transferred and transformed, directly measuring itsabsorption into the material would be impossible. For example, if it was possible to determine thelocation and quantity of energy absorbed from the photons, this would still be insufficient as thatenergy would continue to spread through the release of electrons.To measure dose in an experiment, we must rely on the use of instruments and materials thatdisplay a pronounced response to radiation, such as the build-up of charge, the release of lumi-nescent photons, or the triggering of a chemical reaction. The response must then be carefullycalibrated so that the energy absorbed can be determined from the observed response. However,each of these dosimetric methods come with a number of caveats and contingencies to be aware of.For example, many of these materials are distinctly different from tissue in terms of physical andelectron density and, therefore, require care in generalizing the results to clinical contexts. Other16methods are only applicable in certain dose ranges, or have physical limitations in terms of theirsize or orientation.However, with the power of modern computers, many have attempted to directly access thesubatomic processes underlying the transfer of dose by creating extensive simulation of particle in-teractions. These computerised methods of dosimetry are now the foundation of modern treatmentplans, where algorithms are used to optimise calculated dose distributions, aiming to make the re-sults of each successive calculations better than the previous one. These techniques range fromempirical models that simulate the spread of dose deposited by beamlets of radiation, to full-scaleprobabilistic simulation that track the interaction history of millions of virtual particles.In either case, a thorough understanding of your dosimeter of choice, including the mechanismof its operation and its limitations, is necessary to provide suitable context for any discussion ofthe results. For that reason, this chapter aims to provide a brief overview of the specific techniquesused in this investigation. Our discussion will be focussed upon the methods used in our work i.e.the use of parallel plate ionization chambers, radiochromic films and Monte Carlo calculations.As the results of our experiments and simulations will be compared to dose values obtained usingthe Analytical Anisotropic Algorithm (AAA), as employed by the ECLIPSETM treatment planningsystem, we will also touch on convolution methods for calculating dose. The review providedin this chapter is by no means exhaustive, it is intended only to provide useful context for thedescription of our research methods and results. However, the references cited in these pageswould provide an excellent framework for any who wish to understand these techniques in greaterdetail.172.2 Experimental Dosimetry2.2.1 Ionization ChambersTo begin our review of dose measurement, it is useful to define two terms that are often used tocategorise dosimetry techniques:Absolute Dosimetry Refers to measurements that provide a direct value of the energy absorbedfrom a radiation source, such as a measured increase in temperature (calorimetry) or ioniza-tion charge. The value of dose is then given in reference to a recognised, external standardand in a standard unit, usually Gray [Gy]. In our experiments, we perform surface dose mea-surements using a Markus Parallel Plate ionization chamber. Certain ionization chambersfall into the category of Absolute Dosimeters, and are the basis of the TG-51 protocol, thestandard means of characterizing a treatment linac. However, although this instrument canbe used to obtain exact dose values in Gy, for the purposes of our experiment (as will bediscussed later) we have used it as a relative dosimeter.Relative Dosimetry These measurements rely on some observed characteristic that can not be di-rectly/mechanically linked to the absorption of energy, but whose response to radiation canbe well-established. Relative dosimetry relies on the use of a calibration curve, where mea-surements of the response to known exposures of the photon beam can be used to estimate anunknown dose. Gafchromic film is an example of a Relative Dosimeter. By calibrating thechange in optical density for several films exposed to known doses of radiation, the unknowndose absorbed by a test film can be estimated from its optical density.When matter is exposed to radiation the atoms/molecules within the material become ionized.For the typical range of pressure and electron energies likely to be experience in a clinical setting,the average energy required to produce a single ion pair in air is approximately constant and is18equal to W = 33.97 eV/ ion pair. Therefore, the energy transferred from the radiation beam to avolume of air is directly proportional to the measured ionization charge. From this fact, an absolutedosimeter can be constructed with two parts: an Ionization Chamber, where a well-defined volumeof air is ionized by exposure to a radiation beam, and an Electrometer for collecting and measuringthe resulting charge.Of course, the reality is more complicated than the simple idea described above. In Chapter 1,it was established that the deposition of dose from a photon beam is a two-step process. As such,the ion pairs measured within the chamber are unlikely to be the product of photon interactionswithin the gas, but are instead the results of energy lost from electrons originating within the wallsof the cavity. Therefore, the dose value ascertained from the measurement of charge within thegas must be related to the dose absorbed by the cavity walls by a conversion factor (the ratio ofstopping powers for the gas and the wall materials).Even once the dose absorbed by the cavity wall’s has been established, clinical applicationsrequire a measurement for the dose that would be absorbed by patient tissue rather than wall mate-rial. Fortunately, it is possible to convert the dose absorbed by the walls to that which would havebeen absorbed by a volume water-equivalent medium (the typical approximation for tissue) if itwere in the cavity’s place. This conversion factor is derived from a ratio of the energy absorptioncoefficients for the gas and water, i.e. the relative abilities for these materials to absorb energythrough photon interactions. However, the applicability of these conversions requires two assump-tions: Firstly, that the chamber walls are thick enough that electrons creating ion-pairs within thecavity could only have originated from the walls and not from the surrounding medium; and sec-ondly, that a condition of electronic equilibrium exists. This latter criterion is necessary to directlyrelate the energy transferred to the walls/medium from the photon beam (i.e. the Kerma,) with doseabsorbed.19The preceding paragraphs begin to illustrate some of the challenges involved in accurate clinicaldosimetry. Even with a well-characterised response to energy deposition, such as the creation ofion pairs in air, a number of corrections are needed to relate the behaviour of a measurement devicein a experiment to that of human tissue in a clinical situation. Other correction factors, in additionto the chamber wall correction alluded to above, include[8, 26]:Replacement Correction To account for the perturbation in electron fluence caused by the pres-ence of the cavity and any resulting shift in the precise point of measurements within thechamber.Electrode Correction To account for differences in material between the chamber walls and thecollecting electrode.Air temperature-pressure Corrections Accounts for differences in environmental factors betweenlaboratory and calibration conditions.Ion recombination Corrections Some ion-pairs that are created by the radiation will recombinebefore they are collected, therefore their charge is not measured, and that energy is effec-tively“missed” by the detector. A correction factor can be applied to account for this loss.Polarity Corrections The response of the dosimeter (the paired ionization chamber and electrom-eter) can differ depending upon the polarity of the bias applied to the chamber. A correctionfactor to compensate for this difference may be required.The necessity of these correction factors can make ionization chamber dosimetry appear “du-bious”. However, there exist established methods for accurately determining these corrections.Careful application of these techniques, using an externally calibrated dosimeter, will result in ac-curate measurement of absolute dose. For a a thorough discussion of these procedures the readeris referred to the AAPM’s TG-51 protocol [8], and to the following texts[26, 29].20As our investigation used a ionization chamber as a relative dosimeter, most of these correctionfactors were not needed and discussion of those that were applied is reserved for the discussionof experimental methods in Chapter 3. Instead, we turn to the use of ionization chambers formeasurement of surface dose.2.2.2 Parallel-Plate Ionization ChambersA major challenge facing the use of ionization chambers in surface dosimetry is the absence ofelectronic equilibrium, which is a necessary condition to clearly relate the measured dose in thechamber to dose in the medium. Another issue is the fact that surface or skin dose is a quantitydefined at a specified plane, whereas ionization chambers collect charge from throughout a volume.In fact, the International Commission on Radiological Protection (ICRP) recommends measuringskin dose at 70 µm from the outer surface, which corresponds to the depth of the basal layer of theepidermis [39]. This depth is far to shallow to be commensurate with a practical collection volumefor a chamber.Despite these issues ionization chambers are still used for surface dosimetry. They use aParallel-plate (PP) geometry, as opposed to the more typical cylindrical set-up. The advantagesof the parallel-plate design is that they can be constructed using thin foils as electrodes, which min-imizes attenuation and scattering of photons as they pass into the cavity. They also allow thin gaslayers to be as used as the collection volume, allowing for greater depth resolution. ExtrapolationPP chambers allow the thickness of the gas layer to be adjusted allowing a series of measurementsat different “depths” from which the dose at 70 µm can be extrapolated. These extrapolation cham-bers are generally considered the most accurate method of skin dosimetry. Unfortunately, a largenumber of measurements are required to create the curve from which skin dose can be extrapolated,which limits their practicality in clinical environments.Another option is to use PP chambers with thin, but fixed, collection volumes. However, theseinstruments come with some unique design concerns and some additional complications. Figure212.1 below shows a simplified schematic of a fixed-separation PP chamber. From this image, the PP isseen to bear some resemblance to a parallel-plate capacitor. As with the capacitor, the electric fieldbetween opposing plates is not strictly aligned normal to the plates as their may be “edge effects”.All ionization chambers determine dose by collecting the charge liberated from a precisely definevolume of air, and so, any bending of the field at the edges will alter this volume and affect thedose values measured. To counter this effect, most PP chambers include a “guard ring”, which isa ring of conducting material surrounding the collection electrode. The guard ring is held at thesame voltage as the collection electrode, so effectively extends the electric field beyond the definelimits of the collection volume and shifting the edges away. However, the guard ring is electricallyinsulated from the collection electrode and so does not contribute to charge collection.Figure 2.1: A simplified schematic showing the key design features of a Fixed SeparationParallel Plate Ionization Chamber.As can be seen in Figure 2.1, the photon beam passes directly through the collection elec-trode of the PP chamber. Therefore, photon interactions will occur within the electrode itself andelectrons may be “kicked” out via the Compton Effect. The loss of these electrons will result inan additional positive current being introduced into the electrometer and will result in inaccurate22dose measurements. This effect is most pronounced in chamber designs featuring thin entrancewindows, thick collection electrodes and small separations between plates. A standard method foraccounting for this issue, which we have employed as noted in Chapter 3, is to measure the chargemultiple times at both positive and negative electrometer bias and then average the results to obtainthe final estimate of charge.One significant characteristic of PP chambers is their well-known tendency to overestimate Per-centage Depth Dose (PDD) in the build-up region. Increased ionization due to secondary electronsreleased from the chamber walls is generally considered to be the principle cause of this effect. Intheir 1985 paper, Nilsson and Montelius proposed several recommendations regarding the designof chambers used for dose measurements in non-equilibrium conditions [35]. These suggestionsincluded: the use of large (relative to plate separation) guard rings to reduce the influence of side-wall electrons, and large side wall angles (relative to the beam axis) which would increase theabsorption of secondary electrons within the walls.However, in addition to these design concerns, it is necessary to apply an empirically derivedfactor to correct PDD measurements obtained using PP chambers. In 1975 Velkey et.al, proposeda series of corrections for application in the build-up region, by comparing the results of a fixed-separation PP chamber to an extrapolation chamber [47]. However, these factors proved to lackgeneralizability as their results could not be accurately applied to chambers of different designs.In 1989, Gerbi and Khan expanded upon Velkey’s work by accounting for additional geometricfactors such as the distance between the side walls and the collection electrode, and obtained cor-rections for several commonly used chamber designs and photon energies[25]. Their method hasbeen utilized in many subsequent studies [9, 10, 37] and is the approach we have adopted in ourinvestigation. The correction formula are presented in more detail in Chapter 3.Each experimental method used to determine dose has strength and weaknesses regarding itsapplication. Although ionization chambers are considered the gold standard regarding accurate23absolute dose measurement, the above discussion makes it clear that they are not without flaws,especially when measuring dose in the build-up region. Therefore, it is always good practise toutilize a second technique (or even more) to corroborate dose measurements. In particular, asmodern radiotherapy techniques allow for shaping’ dose with increasing precision, the ability tomeasure the “distribution” of dose is vital. This feature is the key strength of using Radiochromicfilms in dosimetric experiments, and we shall now discuss this methodology.2.2.3 Radiochromic Film DosimetryThe use of radiochromic (sometimes known as GafChromic) film has much in common with pho-tographic films. In fact, some of the earliest films used for dosimetric purposes were coated ina silver-halide emulsion like those used for black and white photography. As with photographicfilms, radiochromic films are sheets of radiosensitive material that undergo a chemical reactionwhen exposed to radiation.These chemical changes effect the transmission of light through the film. Usually the intensityof light passing through the exposed film is reduced, rendering it more opaque than the unexposedregions of the film. In the case of the EBT3 films used in this study, radiation triggers the polymer-ization of di-acetylene monomers in the films active layer. The change resulting in transmission canbe related to the radiation dose absorbed by the film. The opacity of the film is usually quantifiedby the its optical density (OD) according to equation 1, where I represents the intensity passingthrough the film and I0 is the intensity of the light source in the absence of film.OD = log10(I0I)(2.1)Of course, for dosimetric purposes the quantity of interest is the change in optical densitycaused by exposure to radiation. This can be computed from the intensities of light transmittedthrough the exposed Iexp and the unexposed Iunexp film as shown in Equation 2. Measurements of24OD were traditionally performed with an optical densitometer, which was essentially a coupledlight source and photoelectric cell. The film would be “sandwiched” in between the pair, and thephotocell would measured the intensity of light from the source that was transmitted through thefilm. The more modern method is to use a high-resolution flatbed scanner to perform transmissionmeasurements on the whole film sheet simultaneously, with high transmission corresponding to ahigh (or “bright”) pixel value in the scanned image.∆OD = ODunexp−ODexp = log10(IunexpIexp)(2.2)Unfortunately, the relationship between a film’s change in optical density when exposed toradiation and dose is not consistent or well-characterised and can depend on a number of factorswill be discussed below. Therefore, radiochromic films are a tool for relative dosimetry and must bewell-calibrated to yield useful measurements of dose. Calibration curves are produced by exposingpieces of film to known doses and fitting a response curve describing the relationship between doseand the observed change in OD. This curve is then used to infer unknown dose values from theoptical density of test films.Further information on film calibration can be found in Chapter 3, where the calibration pro-cedures used in our experiments are discussed. For the remainder of this section, we will outlinesome of the factors that can effect the dose response of film, and review the work pertaining tosurface dose measurement with films that can be found in the literature.2.2.4 Factors Effecting Dose Response in FilmThe response of a given sample of radiochromic film to a given radiation dose is, in some ways,unique to that particular sample. Although it can be presumed that a hypothetical element of thephotosensitive material would respond to a given quantity of energy according to some mathe-matical relationship. In reality, the photo-polymerization process is sensitive to a large number of25confounding factors relating to the manufacture of the film, the context of the experiment in whichthe film is exposed to radiation, and to the conditions and method by which the optical density isquantified and calibrated against dose. For a detailed discussion of these factors we recommend thereview by Devic et.al [23] and the manufacturer’s documentation for the EVT3 films[3]. However,we will provide a brief summary below.Time-Dependence Photoinduced chemical changes in the film material are not instantaneous pro-cesses. Once triggered by exposure to radiation, the reaction is initially quite rapid, but therate gradually slows[40]. Clearly, OD measurements that are taken too early, i.e. as thereaction is still proceeding, will not accurately reflect the response and will lead to an un-derestimation of dose. Although a dose error of ¡ 1% can be achieved within 30 minutes ofexposure [22], scanning films after at least 24 hours is the commonly accepted practise.Energy-Dependence The response of a film to a given level of dose can vary with beam energydepending on the chemical composition of the active layer. EBT3 films have been shown tounder-respond at low energies (¡ 50 keV)[15, 40]. However, they demonstrate no significantenergy dependence in the megavoltage ranges typically used for medical applications.Film Orientation For photo-polymerizing films such as EBT3, the active layers consists of long,“needle-shaped” monomers whose long axes are aligned along a particular film axis. Theasymmetric shape of these particles will result in anisotropic light scattering within the film.This will have a strong effect when scanning the film data with a flatbed scanner. Therefore,it is important that all film samples are scanned in the same orientation so that accurate dosecomparisons and calibrations can be made.Batch variance Small variances in the manufacture of radiochromic films, such as slight differ-ences in the thickness of the active layer, can result in notable differences in dose response[23].Films obtained from one batch may display significant under/over response compared to an-26other batch. Consequently, comparisons of optical density cannot be made between samplesfrom different batches. Therefore, each film batch should be separately calibrated and thatexperiments utilise films from the same batch so that accurate comparisons can be made.These are, by no means, a full list of possible conflicting factors that can influence the useof radiochromic films as dosimeters. Environmental factors and exposure to ambient lightcan also have an affect. Therefore, when considered as “pure” dosimeters, they are notthe most ideal instrument to use. If exceptional care is taken in controlling these factors,errors of ¡ 5% can be achieved [23]. However, in terms of spatial resolution, films are vastlysuperior to most other dosimetric methods. The radioinduced polymerization of the filmmaterial is a very localized effect, which allows the film to capture a map of dose intensityand distribution. This is similar to how photographic film maps visible light intensity tocreate an image. The advantages of taking a “dose image” are hard to overstate given thecritical role that controlling the shape of dose-distributions play in modern radiotherapy. Thisability is they key reason why we have chosen to use radiochromic films in our research, aswe shall be mapping the changes in dose distribution caused by bolus-skin gaps (Chapter 5).2.2.5 Films for Surface DosimetryAt first glance, radiochromic films would seem like an ideal instrument for measuring sur-face dose, assuming that the various confounding factors could be controlled. They are thin,flat sheets that can be placed directly upon the surface and provide measurements in a 2Dplane. They are also composed of an organic polymer material that dosimetrically compara-ble to water. However, as with ionization chambers, and most other dosimetric methods, thechallenge of measuring accurate skin dose with film stems from the rapid build-up of dosein the first few millimetres of phantom depth.27As thin as they are, the measurement depth (i.e the location of the active layer) of a ra-diochromic film is typically hundreds of µm from the films surface. As an example, theeffective measurement depth of the EBT3 films used in our investigation was determined tobe 0.0189 g/cm2. This is greater than twice the depth of the ICRP defined skin depth of 0.007cm. Given the high dose gradient in the build-up region, a difference in depth of even tens ofµm can lead to an notable over-estimate of dose.A comprehensive study to quantify this effect, and to suggest possible correction factors,was published by Devic, Seuntjens, and colleagues in 2006[21] . In their study they com-pared the surface doses, measured with three models of radiochromic films (EBT, XR-T andHS), with references PDD obtained using an extrapolation chamber, an Attix parallel-platechamber and Monte Carlo (MC) simulations. In addition, Devic et.al. also performed similarmeasurements on exit doses to determine the accuracy of radiochromic films when appliedto the surface through which the treatment beam leaves the phantom.Their results demonstrate that, due to the difference in the effective point of measurement,surface doses measured using radiochromic films do not accurately reflect “skin dose” i.e.dose at 70 µ depth. For example, for a 10x10 cm2 6 MV field, their EBT films measure asurface PDD of 19.9% compared to the “true” skin dose of 17%. Therefore, to estimate anaccurate skin dose value using EBT film would require a correction factor of 0.854. Thesecorrection factors show some dependence on field size, as films appear to overestimate doseto a greater degree at smaller fields.Another method to obtain accurate surface doses with films is due to Butson et.al, whoproposed using extrapolation determine dose an effective depth of 0 mm [12]. Extrapolationchambers, which are still considered the most suitable tool for surface dose measurement, re-quire a large number of individual measurements, at different plate separations, to create theextrapolation curve. However, films do not suffer this disadvantage as numerous film strips28can be exposed simultaneously. By arranging five film pieces into a “stack”, Butson and hiscolleagues were able to take central-axis dose measurements at multiple depths within thefirst millimetre of the build-up region. A quadratic function was fitted to the film data pointsto produce an calibration curve that was be extrapolated to estimate dose at approximatelyzero depth. Their extrapolated surface PDD for a 10x10 cm2 field was 15±2%, which wasin good agreement with a reference value of 16±1% taken with an Attix PP chamber. Itis worth noting that this reference value represents a measurement from an uncorrected PPchamber, and so the difference between the chamber and film extrapolation values could belarger given the established tendency for PP chambers to overestimate surface dose. How-ever, further measurements within the same article, taken at several field sizes and with bothopen and perspex-blocked beams, indicated that film extrapolated surface dose values weregenerally with 2% of corrected Attix measurements.In 2004, Butson followed this work using radiographic films and extended the method toproduce two-dimensional surface dose profiles using extrapolation [14]. Once again theextrapolated surface doses agreed within 3% of value obtained using an Attix PP chamber.In 2009, Chiu-Tsao and Chan [18] published a similar, but more methodologically detaileddetailed, report on the use of radiochromic film stacks for measuring build-up dose with highdepth resolution, and the extrapolation of surface dose estimates. They reported a surfacePDD of 15±0.7 %, which is in good agreement with Butson’s work. This paper is also worthnoting as it provides a table summarizing the reported values of central-axis surface dose for6 MV, 10x10 cm2 beams, which may be of interest to the reader.The above discussion serves to provide a sufficient background into the experimental meth-ods used within this thesis. However, modern dosimetric is an increasingly computerizedprocess and our focus shall now shift to consider computational methods of determiningpatient dose.292.3 Computer Simulated DosimetryAs in the previous section, our discussion shall focus on the dose calculation methods mostrelevant to our study of the bolus air-gap effect, i.e. Monte Carlo Simulations and theAAA. The latter method is an algorithm created by the Varian corporation for use in theirEclipseTMTreatment Planning System. Although other algorithms may be employed withinthis system, we shall only consider the AAA and so the terms AAA and ECLIPSETM can beconsidered equivalent within this thesis.As with most areas of science, Medical Physics has benefited tremendously from the powerof computation. Dose calculation programs allow for more sophisticated treatment plans thanwould be feasible for humans to perform accurately and without error. Computers are nowat the heart of modern radiotherapy, and have made possible much of the rapid progress intreatment delivery methods. Techniques such as Volumetric Modulated Arc Therapy (VMAT)shape the distribution of dose to match the prescribed Planning Target Volume (PTV) by usingoptimisation algorithms to determine the appropriate treatment delivery parameters.The most accurate method of calculating dose is to model the behaviour of millions of pho-tons, electrons and other particles as they spread through the medium. MC simulations per-form this task stochastically through repeated random sampling, as shall be discussed indetail below. However, this approach requires significant computational resources that haveonly recently become commonly available. A more efficient approach is to model the doseusing analytical and empirically-derived functions, and then building upon these by apply-ing various corrections until a more realistic representation of the treatment is achieved. TheAAA is one of several examples of the latter approach, which have proven to be reliable androbust and are used in most treatment planning cases. However, an approximate approach isonly as valid as its underlying assumptions, and the accuracy of these calculations can suffer30in situations where these assumptions no longer hold, as in non-equilibrium regimes like thenear-surface region.2.3.1 The Analytical Anisotropic AlgorithmBefore discussing the AAA in detail, it is worth discussing how a materially accurate repre-sentation of a patient or phantom can be introduced into a computer program. The subjectis described by a three-dimensional array that serves as a “3D image”. As a common 2Dimage is analogous to a matrix whose member values represents the intensity (brightness)of each pixel, the elements of the 3D array record the mass density of the subject medium.Therefore, the variation of tissues present in the human body are encoded within the changesof density value across the array. The resolution of this model, how smooth and precise theseparation between tissue types can be delineated, is limited only by the geometric size ofeach element, which are called voxels.It should be noted that much of the following overview of the AAA is based upon documen-tation written by Janne Sievinen of Varian Medical Systems, developers of the ECLIPSETMTPS [43].The role of the dose calculation algorithm is to bridge the gap between the predeterminedbeam fluence and the resulting dose to the medium. As stated in Chapter 1, the principle dif-ficulty in relating the properties of a photon beam to dose is the fact that dose is not depositedat the location of photon interactions. Whereas MC would simulate the paths and interactionsof the secondary electrons stochastically, algorithms such as the AAA approximate the spreadof dose by using the mathematical properties of convolution.The general concept behind this approach may be familiar to those well-versed in the be-haviour of simple filters and transformations such as those used in medical imaging. At ahigh-level, the medium can be considered as a system that takes a certain input, the energy31transferred from photon interactions, and processes it to produce an output, dose. A well-known result from the theory of such transforms is that the output signal can be representedas the convolution of the input signal with the systems impulse response. The impulse re-sponse is the systems output in the special case of an input signal that is infinitesimal in sizeand duration e.g. a point source. In our analogy, such a signal corresponds to the total energytransferred, from the beam, into a single voxel. The resulting spread of dose into the sur-rounding voxels forms the impulse response, which is approximated by analytical functionscalled scattering kernels.This use of convolution as a means to calculate dose is the foundational element of AAAand many similar methods. Computers can perform very rapid convolutions using FourierTransforms, making the approach extremely efficient and fast-enough for routine clinical use.Therefore, a large portion of the “work” in these programs is dedicated to approximating theproperties of the linac in terms of familiar functions (such as linear combinations of Gaussianor exponential curves) that are amenable to convolution. The main “selling point” of the AAAin particular, is the use of detailed MC simulations and experiments to establish a database ofinformation, which is then used to scale and correct the functions according to each specificclinical situation.Determination of these empirical functions is performed by a process within the AAA calledthe configuration algorithm. The configuration algorithm recreates the properties of a spe-cific treatment unit, specifically the fluence and energy spectra of the photons and electronscomposing the beam. These parameters are derived from both experimental measurementsand MC simulations. MC is used to determine baseline information such as the photon energyspectrum and the beam intensity profile, then these functions are adapted to match dosimetricdata as measured in a water-equivalent medium. The initial MC simulations are performedusing a detailed virtual recreation of a given linac, and the experimental results also come32from the same machine, therefore the modelled beam is specific to that unit. The resultingparameters are stored and retrieved during treatment planning for use in the dose calculationalgorithm. The parameters of the kernel functions are also determined by MC and adjustedto the clinical setting according to the stored characteristics of the beam, and the physicalproperties of the medium.As the patient is represented as an array of individual volume elements, so the treatment fieldis considered as composed of smaller, linear elements called beamlets. Ray-tracing is usedso that the boundaries of each beamlet are commensurate with the angle of beam divergence,and the voxel of the patient are redrawn to match. The properties of each beamlet are thendetermined from the parameters established by the configuration algorithm and tailored toaccurately describe the given clinical context. In the AAA, each beamlet is actually composedof three parts representing the primary photons generated from the beam source, the extra-focal photons produced by the flattening filter or collimators, and the electrons present in thebeam.This information is then used to determine a function estimating the total energy released ineach voxel along the beamlet path. This is our “input” signal, which is then convolved withthe appropriate scattering kernels, across the whole phantom, to determine the distributionof dose.An important feature for any clinical dose calculation program is the ability to accuratelyaccount for the heterogenous nature of human tissue. A radiation beam passing through apatient’s chest may encounter numerous inhomogeneities such as; regions where the anatomyresults in areas of varying tissue thickness (e.g. a field partially covering a patient’s breast),or structures with higher (bones) or lower (lung) electron density. Although, computationalefficient the use of simple functional forms to model the behaviour of a treatment field intissue can encounter difficulties in adapting to changes in anatomical density. The AAA ad-33dresses this challenge by rescaling the properties of each beamlet, and those of the scatteringkernels, according to the local density [43]. For example, the dependence of a given func-tional form on the depth z is reparameterised in terms of the radiological depth z′ accordingto:z′ =∫ t0ρ(t)ρwaterdt (2.3)There is some disagreement within the literature regarding the effectiveness of this correctionmethod based. Several studies have indicated that the AAAs treatment of inhomogeneitiesprovide satisfactory accuracy in determining dose [43, 46]. Others have indicated notablediscrepancies [7, 41]. The interests of our work focus on the treatment of surface doses andextreme inhomogeneities (i.e. air gaps). However, all of the published investigations relevantto that topic use MC as a ‘gold-standard” reference in determining the accuracy of their AAAresults. Therefore, it is worth briefly discussing the MC method before considering thesestudies.2.3.2 The Monte Carlo MethodIn physical systems, many of the properties than can be observed, measured and treatedmathematically actually arise from the random actions of particles on the atomic or molecularscale. For example, changes in temperature or the diffusion of a gas through a volume bothoriginate in the random motion of particles driven to seek a lower energy state. As shownin Chapter 1, the dose deposited by radiation into some medium is also a gross quantity thatis a consequence of the random interactions of billions of photons and electrons. However,whereas temperature changes or diffusion can, in some cases, be treated using well-knowndifferential equations, the transfer of dose does not lend itself to a straight-forward analyticaltreatment. In cases such as these, the power of computation can be harnessed to simulate34the underlying random events directly and properties such as dose are determined throughaveraging the “lives” of millions of simulated particles.Algorithms that make use of random samples to solve intractable mathematical problems aregenerally known as Monte Carlo Methods, after the famous casino in Monaco. In thesemethods the history of some element, say a particle, from its generation to its eventual ab-sorption into the medium is entirely determined by the “roll of a die”, or more accuratelyby a random sample from the appropriate probability distribution. To provide a more con-crete example of this method, we shall consider how the movement of a particle might bedetermined in a typical MC simulation.Consider a photon of energy E, moving in a given direction through a medium with absorp-tion coefficient µ(E). The probability of this photon travelling a small distance x beforeundergoing a random interaction process is given by:p(x) = µ(E)e−µ(E)x (2.4)Given this, the probability that the photon will travel any given distance between 0 and x isgiven by the cumulative distribution function, which can be obtained by simple integration.P(x) =∫ x0mu(E)e−µ(E)xdx = 1− e−µ(E)x (2.5)At this point in our simulation we can obtain a suitable “guess” for the value of P(x) bygenerating a random number R from within the range 0 < R≤ 1 i.e:R =∫ x0mu(E)e−µ(E)xdx = 1− e−µ(E)x (2.6)35From this relation we can determine the distance our simulated photon will move commen-surate with the randomly supplied probability R.x =1µ(E)ln(R) (2.7)The coordinates of the photon within the medium are then updated such that it can be con-sidered to have moved a distance x along its original direction of motion. Having reachedits new location we can determine which interaction it will now undergo using another “dicetoss”.As can be seen in Figure 1.1, there exists a comprehensive body of empirical data relating theprobability of a given interaction event (as measured by the mass attenuation coefficient σ )with the photon energy. The probability of, say, a Compton Scattering interaction occurringrather some other mechanism can be determined from this data as follows:pC =σCσtotal(2.8)Where σtotal is determined from the sum of the mass attenuation coefficients for all relevantinteractions. We can map the probability of an interaction onto a range between between0 and 1 as shown schematically in Figure 2.2. In essence, the probability space is splitinto “bins” whose relative size depends upon the energy of the photon and the attenuationproperties of the material. Once again a random number 0 < R≤ 1 is generated and the binthis number lands in determines the interaction event undergone by the photon.36Figure 2.2: A schematic illustrating how mass attenuation data can be mapped into a prob-ability in the range [0,1]. MC algorithms use a randomly generated number R, whoseplace in this range is used to determine the interaction of a simulated photon.The above discussion illustrates the key mechanics of how random number can be used tosimulate the physics of photon transport in a medium. This process is repeated in variousforms to recreate the “history” of a given photon. In scattering events, the new direction ofthe photon can be randomly determined in line with established theory such as the Klein-Nishina formula. In Pair-production or Photoelectric interactions, the simulated photon canbe “terminated” after triggering the production of simulated electrons whose behaviour arealso modelled as a succession of random processes. With modern computer power, the livesof millions of virtual particles can be recreated. After each event, the energy transferredfrom each particle to the medium is recorded. Therefore, by averaging over a sufficientlylarge number of the distribution of dose in the medium can be accurately calculated.The applications of this method are vast as it models particles transport directly using readilyavailable material properties such as absorption coefficients and cross-sections. With suffi-cient information regarding the geometry and materials of the machine, a virtual model ofthe treatment linac can be constructed. Therefore, MC can accurately reconstruct the be-haviour of an actual radiotherapy unit in clinical use, rather than requiring an approximationof a treatment beam. Similarly, using tissue density information available through high-resolution medical images (such as a CT scan) an accurate 3D model of a patient can beconstructed for use in MC simulations. With accurate modelling of both the linac and the37patient, MC can be used to calculate and predict dose distributions for individual treatmentplans.Accurately recreating the history of single particle, through multiple steps of translation, in-teraction and energy transfer processes, requires a substantial number of individual calcula-tions. When this processes is repeated for the large number of particles necessary to producea statistically accurate model, the process quickly becomes “expensive”. The high cost ofthese simulations is the primary weakness of MC methods. The time taken for to complete asimulation makes makes the method impractical for use in routine treatment planning. Evenwith access to a distributed computer network, computation time can still be significant, andcompetition for limited computer resources between treatment plans can exacerbate this de-lay. Of course, not all institutes have access to such computing clusters. For smaller andmore remote centres and hospitals in the developing world regular use of MC simulations arenear impossible. As such, more approximate but computationally tractable methods such asAAA still have a major role in radiotherapy.At the point a clear distinction between MC simulated linacs and their real-world counter-parts must be made. In the MC algorithm, the number of particle histories, whether millionsor billions, has no relation to the properties of the simulated beam. In real linacs the intensityor duration of the treatment, and thus the dose delivered, is related to the rate and numberof electrons striking the target at the beam source. For MC beams, a larger number of his-tories produced greater statistical accuracy but does not map to the properties of the beam.Therefore, it is not a simple task to determine absolute dose values using MC.However, Popescu et.al published a method for calculating absolute dose with MC in 2005[38].A key aspect of their approach was their choice of the BEAMnrc and DOSXYZnrc codes,developed by the National Research Council of Canada, to perform their simulations. Afterperforming a dose calculation, these programs normalize their estimated dose values by the38number of initial histories, essentially reporting the dose produced per particle. Therefore,it is possible to determine absolute dose provided the dose at any given point in the mediumcan be related to the initial number of particles. Unlike experimental dosimetry, MC simula-tions provide complete freedom upon where you choose to “score” the dose, and so Popescuwas able to calculate the dose (per particle) to the monitor chamber of his virtual linac. Asthe dose to the monitor chamber is used to define the linac’s Monitor Units, a relationshipbetween the number of particle histories and monitor units could be established. In clinicalenvironments, the TG-51 protocol is used to empirically determine the relationship betweendose to a set reference point (in water) and a linac’s monitor units. Popescu and his col-leagues recreated the benchmark tests of the protocol using MC, effectively calibrating thevirtual linac, determining the dose per monitor unit. Combining all of these elements a sim-ple conversion factor was derived, allowing absolute dose at a given voxel to be predictedfrom the prescribed monitor units of simulated treatment plan.The 2005 paper by Popescu et.al, it also especially relevant as the work was performed atthe BC Cancer Agency’s Vancouver Centre. The methods described in this article form thefoundation of the MC system currently used for treatment planning and Quality Assurance(QA) at the BCCA, including the work described in this thesis.2.3.3 Monte Carlo for Surface Dose CalculationIn contrast to most experimental methods, or many other dose calculation algorithms, MCdoes not rely on assumptions of equilibrium or fits to empirical function. As the behaviour ofeach particle is modelled directly, the absence of equilibrium between the transfer of Kermaand the deposition of dose arises naturally and is accounted for within the models. Likewise,particle transport across tissue inhomogeneities are modelled directly, and the properties ofthe local medium are considered, via sampling from appropriate probability distributions, at39each MC step. Therefore, inhomogeneity corrections are unnecessary. This makes MC is anideal tool for investigating dose in the build-up region or in bolus-surface air gaps.In fact, very little literature appears to question the efficacy of MC simulations in addressingsurface doses. Attempts to validate MC results in the build-up region, by comparison of cal-culated PDD with ionization chamber measurements, showed excellent agreement to experi-mental values for 6 MV beams[5]. At 18 MV, some small discrepancies between simulationand experiment were observed in several studies. The scale of the observed anomaly was ingeneral very small, and was only of notable consequence in the build-up region where high-dose gradients can amplify the effects of small differences. After several possible causes forthis behaviour were investigated, the general verdict within the literature is that the effect isnot due to the MC simulations but rather due to error in how the chambers were representedwithin the simulations [28, 33].The most common use of MC simulations within the literature concerning surface dose de-termination, appear to be for additional validation of experimental methods. Earlier in thisChapter we discussed how common dosimetry methods, specifically PP chambers and ra-diochromic film, tend to overestimate surface dose. Several studies have utilised MC simula-tions to provide an estimate of the “true” surface dose so that the scale of any overestimationor necessary corrections may be determined[9, 21, 37].MC is not without its flaws. Given the large number of researchers working on extending andimproving the application of MC simulations to radiotherapy, it would be quite unreasonableto expect that there is a single, unified method for performing these calculations. Thereare several competing programs to choose from, multiple different algorithms for treatingcertain aspects of particle behaviour, and a range of settings that define the “depth” anddetail to which the particle histories are reproduced. Whenever a simulation is run, the useris given the opportunity to adjust various parameters and fine-tune the calculation to their40needs. Exploration of the literature reveals that the choice of these parameters can effect theresults of the MC, particularly in the build-up region.At a conference in 2009, Takeuchi et.al presented the effects of user-specified parameters ondoses in the build-up region calculated with the EGS5 code [45]. The two parameters studiedwere the Electron Cut-off Energy (ECUT) and electron production cut-off energy (AE). TheECUT value specifies a lower bound for electron energy, below which an electrons history isterminated and the remaining energy is deposited locally within the medium. The value ofAE specifies the minimum energy transfer necessary to trigger the production of a secondaryelectron. The choice of these values represent a trade-off between accuracy and computingtime. Higher values will reduce the CPU cost by reducing the number of calculations thatcomprise an electron history, and reducing the number of electrons that must be calculated.However, a value that is too high can miss key events and reduce the accuracy of the model.Typical values for both ECUT and AE are 0.521 or 0.700 MeV[31, 38].Takeuchi’s results show that a choice of larger value thresholds (ECUT = AE = 0.700 MeV)can lead to significant underestimation of surface PDD compared to simulations using moreaccurate limits (ECUT = AE = 0.521 MeV). The difference in dose values reached as highas 14% for a 4 MV beam and a 30x30 cm2 field. However, this discrepancy is significantonly within a depth of 0.1 mm, and their work also show that a higher value, for either AEor ECUT, can result in a two-fold improvement in computing efficiency. Therefore, theirrecommendations are that the lower value limits are only necessary in special cases whenaccurate determination of surface doses are important (such as the current study).Further work on this topic was published by Kim et.al in 2012[31]. This article is morerelevant to our research as it utilises the same MC code, BEAMnrc and DOSXYZnrc, asour work. It is also a more extensive study that the work presented by Takeuchi et.al, as italso explored effects arising from the users choice of which algorithms are used to model41the transport of electrons. A Boundary Crossing Algorithm (BCA) is used to transfer thesimulated electron across voxel boundaries within the virtual phantom. An Electron Step-ping Algorithm (ESA) is used perform small deflections in an electrons path, simulating themultitude of small elastic collisions that will cause an electron to deviate from its line ofmotion. As with the values of threshold energies, the choice of which precise algorithm isused reflects a compromise between accuracy and efficiency. The reader is referred to theDOSXYZnrc documentation for further details on these algorithms and the options available[49].Kim’s results show that choice of electron transport threshold values and algorithms can re-sult in differences of calculated surface doses as high as 10. In agreement with Takeuchi’sresults, Kim found that these effects are highly surface specific and that computational effi-ciency should only be sacrificed in cases where high accuracy in surface doses are required.In such cases, ECUT = AE = 0.521 MeV is recommended. With regards to the choice ofESA, either PRESTA-I or PRESTA-II, it was found that the former provided a significantimprovement in computing speed but had little effect on calculated surface dose. In contrast,the choice of BCA was found to be more influential, and Kim recommends using the EX-ACT algorithm, as opposed to PRESTA-I, to yield more accurate results despite the loss ofefficiency.2.3.4 Comparison of Dose Calculation Algorithms Regarding Surface DosePreviously in the chapter, we discussed the operating principles of the AAA algorithm as em-ployed by the ECLIPSETM TPS. One of the strongest advantages of the AAA over some otherdose-calculation methods is the use of MC simulations and experimental data to optimizemathematical models of the treatment beam in order to provide a more accurate recreationof a given treatment unit. The drawback to this method is that resulting calculations will be42biased by any methodological flaws in these simulations and experiments. As we have dis-cussed, due to the high dose-gradient in the near-surface region, accurate dosimetry withinthe first mm of phantom depth can challenging. or For example, the necessary dosimetricdata required to configure the AAA is most likely obtained using cylindrical ionization cham-bers which are unsuited to measuring accurate build-up dose. The issue of “effective pointof measurement” can apply even to MC methods, where the results can depend on the size ofthe phantom voxels near the surface (this is a topic we will return to in Chapter 3).The research evaluating the performance of AAA in calculating surface and skin doses islimited, and in most cases MC results are considered the “gold-standard” of comparison.Several of the relevant studies are primarily aimed at the study of tangental treatment fieldssuch as commonly used in the treatment of breast cancer. A 2009 study by Panetierre et.al.compared AAA and MC results in the build-up region for a cylindrical phantom [36]. AAAwas found to consistently underestimate near-surface dose (for 6 MV) beams over a range ofbeam angles between 15-75◦. However, the authors dismissed the differences as clinicallyirrelevant, as the deviation is only significant for depths ¡ 1 mm, and even then are still withinallowed tolerances. In contrast, similar work by Chakarova and colleagues found generallygood agreement between AAA and MC for all depths, including the near-surface region [17].Another study, by Chow et.al, considered treatment beams tangentially incident upon a cubicsolid-water phantom. In this case, the central axis of the field was parallel to the surface planeof the phantom [20]. They calculated doses within a 2 mm thick slab at the phantom surfaceand found that AAA produced significantly higher values than MC, with the effects beinggenerally worse for higher energies and small fields. Their final conclusion that AAA, anda related algorithm the Collapsed Cone Convolution method, cannot produce accurate dosepredictions for depths <2mm.43More recent interest in the application of Stereotactic Body Radiotherapy (SBRT) has ledto further review of the accuracy of dose calculations due to the small fields and high-dosefractions used in the procedure. In a conference proceeding from 2014, Cho et.al. com-pared skin dose values predicted using the AAA with MC and experimental measurementsperformed with EBT2 films and an Attix PP chamber [19]. Although MC results were foundto be up to 3.5% higher than Attix measurements, skin dose values calculated with AAA werefound to overestimate the experimental data by a much higher degree. For a 6 MV 10x10cm2 field, AAA predicted surface PDD to be 40% compared to a chamber value of 16%.A tendency for AAA to underestimate surface dose was also observed by Walters et.al in aninvestigation of SBRT treatments applied to canine limbs [50]. An interesting aspect of thisreport is that the degree of deviation, between experimental and AAA results, was observed tobe dependent on the dimensions of voxels used in the dose calculations, with smaller voxelsfound to be more accurate.A key point that we have emphasised throughout this chapter is that accurate determinationof dose in the near-surface region is a persistent challenge in dosimetry. The presence ofnon-equilibrium conditions and a high dose-gradient makes obtaining consistent and unam-biguous results difficult. As we have seen, the issue of “point of measurement” is a recurringproblem the effects both experimental and computerized methods. Given the rapid build-upof in the first few milimetres from the surface, measurements using different instruments,e.g. PP ionization chambers and radiochromic films, are effectively taken at different depthsand so can have significantly different results. Computer simulations using voxels of dif-ferent sizes is analogous to this situation with similar results. Using multiple techniques inan experiment, so that the results can be cross-validated, is an almost ubiquitous practise indosimetry. However, this approach is much more challenging when the doses of interest areat the surface. We attempt to address this concern in the current investigation by normaliz-44ing each measurement using a suitable reference value obtained using the same method, andtherefore we consider the relative effects of increasing bolus-skin distances. We will nowdiscuss our methods in detail in the following chapter.45Chapter 3Validation of Monte Carlo Methods3.1 IntroductionMany modern radiotherapy techniques such as, IMRT, VMAT, and others, rely on inverseplanning. To create a suitable treatment plan using this method, accurate computerised dosecalculations are critical. These calculations must account for the many compounding vari-ables present in the treatment room, including the application of bolus and the effects of anygaps between the bolus and the patient’s skin.Many commercial Treatment Planning System (TPS)s, such as ECLIPSETM, use convolution/-superposition algorithms to calculate dose. As described in Chapter 2, these programs usedensity-based rescaling to account for heterogeneities in the medium, presumably, includ-ing air gaps[20, 43]. Conversely, MC methods directly simulate the behaviour of “virtual”photons and electrons, determining the occurrence of interactions and energy transfer eventsusing probability distributions based upon well-established physics. MC is widely consid-ered the more accurate technique but comes at a higher computational cost, and so is less46widely available [7, 38]. The comparison of these algorithms’ ability to accurately simulatethe effects of bolus-skin gaps, is a central question in this thesis.The work in this thesis also aims to lay the foundations for future exploration into both theessential physics and the clinical relevance of any gap effect. If effective, these simulationswill also form the basis for a “virtual laboratory”. In this space, individual parameters such asangle of incidence, beam shape, Multi-leaf collimator (MLC) collimation, and bolus shapescan be individually isolated and studied in an idealized environment. After exploring thiswide parameter space, these findings can be applied to clinical situations for planning andquality assurance.However, any computational tool is only useful if it can be shown to accurately simulate thephysics of the scenario. Before we can use these techniques to explore the unique circum-stance of bolus air gaps, it is necessary to confirm their results in a more standard situation.In this Chapter, we will discuss our methods of validating our simulations by compar-ing calculated PDD curves, from both MC and Eclipse, with experimental data obtainedwith Gafchromic film and a Markus R© parallel-plate ionization chamber (manufactured byCNMC+, USA). For these studies, we used an open 6 MV beam, incident on a cubic water-equivalent phantom. This set-up was chosen for several reasons: Firstly, measuring PDDcurves in these conditions is a standard test performed during the commissioning and qualityassurance of a clinical linac[8]. Secondly, this method has been used several times in the lit-erature as a means of validating simulations[16, 20, 38]. Thirdly, the virtual phantoms usedfor this process could be easily adapted to the study of air gap effects by the addition of afloating slab of water to serve as the bolus.473.2 The Design of Virtual PhantomsIn our simulations we have taken the clinical context of a radiotherapy treatment requiringbolus, where a gap is present between the bolus and the patient’s skin, and have simplified itto the most idealized scenario, as follows: A cube of water is irradiated by an open, 6 MVbeam at normal incidence with a uniform slab of water serving as a bolus. The surface of thecubic phantom is positioned at 100 cm distance from the radiation source (an Source-SurfaceDistance (SSD) set-up) and the bolus is placed above. Air gaps are introduced by “floating”the slab above the phantom at fixed distances.This general set-up is illustrated in Figure 3.1, below. The arrangement is essentially avirtual replica of the experiment performed by Khan et.al[30] to study bolus effects, whichwas adopted to provide an established point of reference within the literature.The key element in this model is the construction of the phantom. DOSXYZnrc, the MCprogram used for this study, allows the creation of very simple phantoms [49]. Essentially,the user defines the outer limits of a cubic volume in a Cartesian space. This space is dividedinto voxels by entering the coordinates of each voxel’s boundaries. Once the space has beenvoxelised, the users then “fills” the volume with a material of their choice, i.e. the voxels’mass-density is set to the value corresponding to the chosen substance, which is then used tocalculate the transport of photons and electrons through that voxel. Materials can be assignedto individual voxels or to entire regions within the subject volume. The results are stored asa 3D density matrix in an .egsphant file.48Figure 3.1: Schematic showing the apparatus used for our Monte Carlo simulations. Thephase space source corresponds to the source of the virtual 6 MV linac. Note, that theorigin of the system is defined at the centre of the phantom’s surface. The bolus floats inair above the phantom within the negative -z region. Our measurement points are withinthe phantom body i.e. the +z region. Surface dose is measured at Dsurf, which is locatedin the centre of the voxels immediately below the origin.The virtual phantoms used for our simulations were created using this method, as it wasbelieved to be the best way to create a truly “ideal” phantom. Other methods, such as creatinga phantom from a CT renderings of a cubic phantom and a bolus, or by “drawing” the systemin Eclipse, were either untested or might introduce sources of error such as slight angles in thepositioning of the bolus or non-flat surfaces. By making our phantoms in DOSXYZnrc, wecould ensure that our bolus was perfectly flat and of uniform thickness and density, allowingus to isolate the effects of bolus-surface gap sizes and field sizes alone.49For the purposes of our investigation, a suitable phantom should demonstrate the followingcriteria:1. Simple geometry that can be easily adjusted and allows for a large range of bolus-skindistances.2. Wide enough to allow multiple field sizes to be applied to the same phantom.3. Deep enough the avoid complications to the backscatter in the near-surface region.4. Water-equivalent.5. Can be introduced into Eclipse for treatment planning and AAA dose calculations.6. Total number of voxels in the phantom should be small enough to allow for reasonablecomputation times.7. Simulations should deliver accurate PDD values in the very near surface region.As shown in Figure 3.1, our model is constructed from a 30x30x60 cm3 volume. The upperregion (in the -z range) is filled with air, whereas the lower region (+z range) is made of waterand defines the actual “body” of the phantom. A bolus was constructed by converting a slabof voxels in the upper half, spanning the whole xy plane and with a depth corresponding to1 cm, into water. By reducing the upper and lower z boundaries of this slab, the bolus iseffectively “floated” up from the phantom surface to provide a set range of air gap sizes (g).A new .egsphant file was created for each bolus-skin value studied. If no bolus is present,as in the validation experiments described in this chapter, the entire upper half of the systemremains as air.Finding an appropriate choice of dimensions for the voxels required some trial and error.This is due to the conflicting demands of items 6 and 7 in the above list. To limit the numberof voxels and maintain a reasonable CPU time in a phantom of this size, those voxels need50to be quite large. However, if the voxels are too large the calculated surface dose becomesless accurate. As discussed in Chapter 1, high-dose gradients are present near to the surfacedue to the lack of electronic equilibrium in the build-up region. With large voxels, these gra-dients are averaged out leading to an overestimation of dose. This is analogous to the issuespresented in experimentally measuring accurate surface doses using large-cavity ionizationchambers.Our original design used uniform voxels of 0.25x0.25x0.25 cm3. Monte Carlo simulationsof a 10x10 cm2 field incident on this phantom calculated the PDD at the Dsurf point aas43± 2%. This is high compared values obtained in the literature, which are typically 14-16%, depending on the exact study and measurement method used [12, 21, 25, 37]. It shouldbe noted that with the given voxel size, the depth of the Dsurf point is 0.125 cm, which issubstantially deeper than the standard reference depth for “skin” dose (70 µm). The resultsof our simulations are consistent with available values for the similar depth of 1 mm[12, 21],indicating our simulations are accurate but also that this voxel size is insufficient for the thestudy of surface dose.To achieve accurate surface dose whilst limiting the number of voxels, we decided to usea phantom composed of two different “grades” of voxel size, shown in Figure 3.2. In thenear-surface region, where more fine-grained measurements are required, we use voxels of0.25x0.25x0.005 cm3. After a depth of 1 cm, the voxels are restored to the more standard0.25x0.25x0.25 cm3. Using this format, the measurement depth of the first voxel layer is25 µm, which corresponds to the measurement depth of the Markus PP chamber (0.0025g/cm2)[2] and the second layer is 75µm, which is a good match to the standard for skindepth. At the second layer depth, calculated surface PDD was 19.2±0.14%, which is muchcloser to the values found in the literature.51Figure 3.2: Schematic showing the voxel distribution for the virtual phantom used in our MCsimulations.The use of two different voxel sizes did introduce concerns as to whether results from thetwo voxel grades would be comparable, and if the results could be used to construct a singlePDD curve for the whole phantom without introducing artifacts. This issue was addressed bycomparison to experimental PDD data as part of the validation experiments we discuss laterin this chapter.However, as discussed in the next section, the use of this 2-voxel phantom did introducesome further complications when it was found to be incompatible with the use of the EclipseTPS.523.3 Interfacing DOSXYZnrc and EclipseFor several years, the BC Cancer Agency (BCCA) has utilized an automated process that al-lows MC absolute dose calculations of clinical treatment plans using actual patient data. Theprogram takes treatment plans created in ECLIPSETM and converts them to input files forDOSXYZnrc and BEAMnrc so that a MC simulation of the plan can be performed. In addi-tion, the CT data, used to define PTV and at-risk structures in treatment plans, can convertedto an .egsphant file, creating a virtual phantom of each individual patient.This system was developed in-house as a QA method, with contributions from numerous staffand students at the BCCA, notably Tony Popescu [38], Tony Teke, Alanah Bergman [11] andParmveer Atwal. The whole program is comprised of many subprocesses, each with its ownfunction and methodology, e.g. the particular MC algorithms and error-reduction methodsused, the derivation of coordinate transformsations between ECLIPSETM and DOSXYZnrc“spaces”, implementation of MLC beam-shaping, and a great deal more. The discussion ofthese aspects are far beyond the purview of this thesis and so we will focus our attention onthe particular modifications developed for this investigation.One of the key issues addressed in this investigation was to compare the ability of AAA andMC to accurately simulate the effects of bolus-skin gaps on surface dose. For this purpose,the use of the BCCA’s interface between ECLIPSETM and DOSXYZnrc was an excellent tool.The simple open-beam set-up described above could entered into Eclipse as a treatment planand the dose distribution would be predicted using AAA. The QA script would then be usedto export the treatment plan for MC dose calculations and the results compared.However, although the existing QA scripts include methods for converting patient CT datainto .egsphant files, no process existed to import existing .egsphant files into ECLIPSETM.Therefore, we developed a script in MATLAB to convert our idealized bolus phantoms into53a format that could be introduced into the TPS. The key task of this script is to extract eachplane of an .egsphant phantom and convert it to a CT image slice stored in a DICOM file.The full set of images can be imported into ECLIPSETM and combined into a 3D model,recreating the original phantom.Unfortunately, as mentioned in the last section, the different voxel dimensions within ourphantom proved to be incompatible with conversion to a 3D “pseudo-CT” rendering. Whenconstructing a 3D representation of the subject, ECLIPSETM (and most medical imaging soft-ware) assumes that the image slices are all of equal thickness. Our phantoms have both 0.005cm and 0.25 cm slices along the z axis. The software assumes 0.25x0.25x0.25 cm3 voxelsand so the resulting phantom appears to be stretched out in the z direction. Attempts tocompensate or correct for this effect have proved unsatisfactory.A compromise was accepted where phantoms of uniform, 0.25x0.25x0.25 cm3 voxels wereused to create the original treatment plans, and for AAA dose calculations. However, afterconverting the plan into a DOSXYZnrc input file, the “fine-grade” phantom was used for MCcalculations.Despite the use of two phantom variants, it was not believed that this would affect the plan orthe dose calculation. Although energy is deposited into a medium by the actions of subatomicparticles, dose is a macroscopic property. The phantoms may differ in voxel resolution butthey still represent identical bodies, composed of the same material and of the same size,being subjected to the same treatment under the same conditions. The subject of the inves-tigation has not changed but the scale of measurement is different. Our interest in bolusconfirmation primarily relates to skin dose, where the relevant depths are between 50-100µm. The thin voxels used in our MC phantom reflects a choice of measurement tool moresuited to this scale.54Our approach to addressing this issue had two parts: Firstly, we analysed results over a wide-range of depths so that corresponding data points can be compared. This was achieved bythe comparison of MC and AAA PDD curves as part of the MC validation described in thischapter. Secondly, we concentrated our analysis regarding the treatment of bolus air gaps, onthe discussion of relative effects rather than direct comparison of absolute dose values. Thiswill be elaborated upon further in Chapter 4.3.4 Monte Carlo Simulations and Analysis.In laying the groundwork for MC study of the bolus gap effect, our simulations have focusedon the influence of two key parameters, the distance between the bolus slab and the surface ofthe body, and the field size of the treatment beam. These factors were chosen as the literaturedemonstrates that both variables have an effect on surface dose in the presence of an air gap[13, 30, 44].Virtual phantoms were to represent the following bolus configurations:• No bolus present• Bolus in full contact with the phantom (g = 0)• Bolus with gap sizes of g = 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 10.0, 15.0, 20.0 cm.Four variants of the same open-beam treatment plan were created for each of these phantomsusing a square field of size 5, 10, 15 or 20 cm. Therefore, a total of 44 separate plans werecreated in Eclipse and 44 AAA and MC dose calculations were performed. The flow-chartin Figure 3.3 depicts the key steps used in planning and running each one of these plans inDOSXYZnrc and ECLIPSETM.55Figure 3.3: Flow chart illustrating the process used to create MC simulations from ECLIPSETMtreatment plans using idealized virtual phantoms. Rectangular boxes represent processesand parallelograms indicate output files that would be fed into other subsequent steps.56In all cases, the treatment was to deliver a prescribed dose of 100 cGy to a point located atthe centre of the phantom surface (the Dsurf point shown in Figure 3.1). The PTV was definedto include the entire 30 cm3 volume of the phantom’s “body”. The simulated linac used forboth treatment planning and MC calculations was a Varian Clinac iX and the central axisof the 6 MV beam was incident directly through the bolus, i.e. along the z-axis defined inFigure 3.1.The QA script employed by the BCCA sets the parameters for the Monte Carlo algorithmwhen converting a treatment plan into a DOSXYZnrc input. In using this script to set-up oursimulations we have adopted these values with little modification. The most relevant valuesused in our DOSXYZnrc simulations were:• Number of simulated particles was N = 5x109• Global photon and electron transport cut-off were PCUT = 0.01 MeV and ECUT = 0.7MeV• Threshold for the production of Bremstrahlung photons was AP = 0.01 MeV• Threshold for the production of knock-on electrons was AE = 0.7 MeVThe MC calculated dose for each voxel in the .egsphant phantom forms a dose matrix, whichis recorded as a .3ddose file. The QA script automatically performs 3D Savitzky-Golay filteron this dose matrix to reduce the effects of stochastic noise in the results [27]. This is anexample of a Variance Reduction Technique, such as commonly employed in Monte Carlostudies and full details of this filter can be found here [11]. The script also creates a new.3ddose file containing absolute dose values (in Gy), which are determined by multiplyingthe filtered dose matrix by a scalar conversion factor[38].57Once the AAA dose calculations and 7MC simulations were performed, the results were anal-ysed in MATLAB. Simple scripts were developed to extract and plot key information such asPDD curves, lateral dose profiles and surface dose. These scripts are given in the appendix.3.5 Experimental Validation of Simulated PDD CurvesIt had been stated previously that computerised dose calculations are a useful tool only if theycan accurately predict and reproduce results obtained through direct, physical measurement.To confirm the validity of our MC methods, and to assess the possible effects due to themodifications discussed above, we have compared simulated PDD curves with measurementsobtained using both a Markus parallel plate ionization chamber and EBT3 Gafchromic films.With regards to surface dose measurements, most sources consider extrapolation ionizationchambers to be the most accurate and reliable method[21, 25]. However, in the absenceof such an instrument parallel plate chambers have been shown to produce accurate resultsprovided a suitable correction factor is applied[25]. Therefore, we selected a parallel plateionization chamber as our primary tool for our validation study and later measurements ofsurface dose.Radiochromic films are widely considered a less reliable dosimetry tool [23], due to issuesconcerning variability between film sheets and a strong dependence on processing and analy-sis methods. However, unlike ionization chambers that can only report dose at a single point,films can be used to measure the distribution of dose across a plane. This ability was con-sidered particularly relevant for later experiments concerning the effect of bolus-skin gapson lateral surface dose profiles, and so, EBT3 films were also used during our validationmeasurements.58The diagrams below illustrate the apparatus used for PDD measurements, with PP chamberand EBT3 films. A 6 MV Varian Clinac iX was used to irradiate the phantoms with a totaldose of 100 MU, delivered at a rate of 600 MU/min, using square fields of 5, 10, and 15 cm.Figure 3.4: The experimental geometry for PDD measurements with a Markus parallel-plateionization chamber59Figure 3.5: The experimental geometry for PDD measurements with EBT3 radiochromicfilms.PDD measurements were conducted in a solid-water phantom, with the exception of a 1cm thick slab of acrylic which was used to hold and surround the Markus chamber. Inthe absence of additional build-up material the point of measurement was taken to be theinner surface of the chamber entrance window, at a depth of 0.0025 g/cm2[2]. Measurementdepths between 2 mm to 16 cm were obtained by placing layers of solid water upon the60chamber, and adjusting the couch height to maintain a SSD of 100 cm. The solid-watersheets available were too thick to conduct measurements at depths z < 2 mm, therefore,sheets of EBT3 films (from an expired batch) were used to provide the necessary build-up atthis range. The effective thickness of a single EBT3 film was estimated to be 0.0378 g/cm2,based on information from the manufacturer’s user guide[3]. Therefore, for example, placingtwo sheets of film over the Markus chamber results in an effective measurement depth of 2× 0.0378 g/cm2 + 0.0025 g/cm2 = 0.0781g/cm2.The charge Q(z) within the chamber cavity was measured with an electrometer. For eachdepth point (z), three charge values were measured for both +300 V and -300 V. The meanabsolute magnitude of all six electrometer measurements, was used as the final value ofcharge accumulated. The standard error was used as a measure of the stochastic error inthe charge value, which was combined with an estimated electrometer error of 0.01 C, usingstandard methods. The average relative uncertainty in the charge measurements was lessthan 0.3 %.Each experiment run, for both instruments and all field sizes, included a measurement at 1.5cm depth - the standard value of zm for 6 MV beams. The charge collected at this depth wasassumed to be the maximum charge, and PDD was calculated as the ratio:P′(z) =Q(z)Q(zm)×100% (3.1)In Chapter 2, it was noted that PP chambers have been shown to overestimate PDD in thenear-surface region and that this effect can be accounted for by the use of a correction factor.For our work we have utilised the correction derived by Gerbi and Khan, where the correctedPDD P′(z) can be calculated from the raw data P(z) using Equation 3.1[6, 25].61P′(z) = P(z)− ε(0)d exp(−α zzm)(3.2)In this expression d represents the separation between the parallel plates of the chamber,which was 2 mm for the Markus chamber[2]. α is an empirical constant determined, byGerbi and Kahn, to be approximately equal to 5.5. ε(0) represents the degree to whichthe chamber can be expected to overestimate the PDD at the surface and can be determinedfrom the Ionization Ratio (IR = 0.664) of the linac and the distance between the sidewalland collection electrode (C = 0.35 mm) for the chamber used. Gerbi and Khan determinedthat their correction method typically provided PDD values within ≈ 1.3 % points of theirextrapolation chamber results. This value was taken as an estimate of the systematic errorof the correction process and, together with the value of the error in P(z), indicated that theabsolute uncertainty our corrected Markus PDD is less 1.4%.ε(0) = (−1.666+1.982 IR)× (C−15.8) (3.3)For film measurements, 2x3 cm2 pieces of were cut from a single sheet of EBT3 film. Carewas taken to ensure that the long axis of each piece coincided with the long axis of theoriginal sheet to avoid artifacts that may be caused when comparing films of different orien-tations. Unlike ionization chamber measurements, where measurements at each depth mustbe performed individually, all films used to construct our PDD curves could be irradiatedsimultaneously, as shown in Figure 3.5. The edges of each film piece were firmly tapedto the underlying solid-water to prevent air-gaps, which are known to affect the dosimetricaccuracy of the film.As with the Markus chamber, sheets of EBT3 were used as build-up material to allow mea-surements at depths under 2 mm. Inspired by the relevant work of Butson.et.al [12, 14], we62created a stack of four film pieces and placed it directly on top of the phantom with its centrealong the central-beam axis. Using this approach, each film within the stack provided a valueof P(z) in the near-surface region of the PDD curve. The plane of measurement within eachfilm was assumed to be at the centre of the active layer, at an effective depth of 0.0189 g/cm2within the film. Therefore, the depth of measurement for a given piece, within the stack, was0.0189 g/cm2 plus the total thickness of the film of the film layers on top. As with individualfilms, the edges of the stack were bound with masking tape to minimize air gaps.The beam conditions for irradiation of the films were the same as those used for the Markuschamber measurements.For use in dosimetry, the optical density of a batch of film must be calibrated by exposure ofa sample sheet to known doses. The linacs in use at the Vancouver centre are calibrated toprovide an output of 1 cGy/MU, delivered at zmax and using an SAD geometry. Therefore,the measurement plane was adjusted so that the films were at a distance of 100 cm from thesource and 1.5 cm of solid-water build-up was placed on top. Three reference films wereused, each being exposed to doses of 0, 80 or 200 cGy.The EBT3 films were stored in opaque envelopes for a minimum of 24 hours before be-ing digitized using a Epsom 10000 XL flatbed scanner. The long axis of the scanner wasaligned perpendicular to the long axis of the film pieces. FilmQA Pro software (AdvancedMaterials, Ashland) was used to create dose maps from the scanned images. The conversionto dose is performed by identifying and selecting regions of interest on the reference films.The software determines the optical density in each of these regions and assigns the correctcalibration dose in cGy. From these reference points, the software dose for each pixel of theimage was determined by interpolation using a function fitted to dose-response curve deter-mined for the film batch used. A suitable response curve was already present in the softwareat the time of our analysis and so additional calibration experiments were unnecessary. This63curve had been created by Joel Beaudry, a Physics Assistant at the BCCA Vancouver centre.The resulting dose maps were exported as .tif files and analysed in MATLAB.The dose received by each film strip was determined by averaging the pixel values acrossa 10x10 pixel2 region. These squares were centred at the midpoint of each film piece toavoid possible artifacts, such as scratches or stress cracks, that could be present at the cutedges of each piece. Before averaging the dose within each region, the influence of “spikes”were minimized by applying a 2D median filter. As with the Markus chamber measure-ments, doses measured at a depth of 1.5 cm were taken to be the maximum dose and used todetermine the PDD for all other data point.The standard error of the mean dose for each depth was typically less than 0.5 cGy. Thesystematic error due to the mapping of optical density to dose, as performed by FilmQAPro, was estimated using the RMS difference between the mean dose of the reference filmsand their known dose values. This error was found to be ≈ 0.9 cGy. When combined andpropagated using standard methods, this resulted in typical absolute uncertainties in the PDDvalues of ≈ 2.0%.3.6 Results of the Validation ExperimentsFigure 3.6 shows simultaneous plots of PDD curves obtained using MC, ECLIPSETM, EBT3Gafchromic films and a Markus parallel-plate ionization chamber for all three field sizesstudied. These results depict the distribution of dose along the central-beam axis in the ab-sence of any bolus material. It can be readily seen from these curves that our MC simulationsdisplay excellent agreement with experimental measurements. This is especially prominentfor the comparison between the Markus chamber and the MC data. Film data also showsgood general agreement with the simulations, however, some data points are clear outliers.Although care was taken to account for systematic effects known to effect the dose response64of films, such as their orientation or their scan direction [23], the behaviour of some filmpieces could still have been perturbed. One possible cause of this could have been the pres-ence of an air gap between the film and the solid water medium, despite the use of tape to tryand assure full contact.65(a) 5x5 cm2(b) 5x5 cm266(c) 5x5 cm2Figure 3.6: Comparison of PDD curves, obtained using a Markus parallel plate chamber,EBT3 films, MC, andAAA for 5x5, 10x10 and 15x15 cm2To allow for a more thorough discussion of the results, Figure 3.7, shows the build-up regionsof the PDD curves depicted above. At this scale, the most notable feature is the divergencebetween AAA results with experimental and MC data in the near-surface region. The AAAresults can be seen to significantly overestimate the PDD, relative to MC, in the first voxel.The difference between AAA results at 0.125 cm and MC results, at the comparable depth of0.1225 cm, was 8.3%, 11.7%, and 13.5%, for 5,10 and 15 cm2 fields, respectively.67There are several possible reasons for this discrepancy. The first is that the phantoms usedfor the ECLIPSETM calculations possessed larger surface voxels than those used for MC cal-culations, and so the larger dose gradient in the build-up region would have been averagedover a greater depth. However, MC calculations performed with the larger (0.25 cm3) voxelsyield a surface PDD of ≈ 47% at 0.125 cm depth with a 10x10 cm2 field, which is consistentwith literature results of 43% for 1 mm[21] but still lower than the AAA predictions of 61%.Another reason for ECLIPSETM’s overestimation of surface dose, is that the beam model usedby the AAA algorithm is dependent upon empirical corrections based upon clinical beam data,typically acquired during commissioning and calibration of the machine[43]. Therefore, theresults of the algorithm are, to some degree, contingent upon the accuracy of these measure-ments. Using an ionization chamber that is unsuited to surface dose measurements, such asa Farmer chamber, or if corrections such as the Gerbi-Khan method are not applied, couldlead to a systematic overestimate of dose that is specific to the surface. This is illustrated bycomparing our MC and ECLIPSETM results with QA data acquired using a raster scanned ion-ization chamber ( a IC 10 Wellhofer thimble chamber) in a water tank (Figure 3.7(d)). Thisdata was provided by Vancouver Physics Assistant, Vince Strgar. The AAA results show fairagreement, which adds weight to our premise that the entered beam data could result in anoverestimate of surface PDD.In general, the results of our MC calculations show excellent agreement with experimentaldata, despite the modifications we have made to the standard simulation process. The MCsimulations accurately mimic the physical behaviour of a 6 MV beam incident on a water-equivalent cube and so can be considered valid for further use in the study of bolus air gaps.68(a) 5x5 cm2(b) 10x10 cm269(c) 15x15 cm2(d) 10x10 cm2 with OmniPro dataFigure 3.7: Comparison of the build-up region for PDD curves, obtained using a Markus par-allel plate chamber, EBT3 films, MC, and AAA for all field sizes.70Chapter 4The Effects of Bolus-Skin Gaps onSurface Dose4.1 IntroductionAccurate and efficient dose calculation underpins all aspects of radiation treatment, fromensuring patient safety to QA. High-precision dose-sculpting methods, such as VMAT, requirehigh-quality dose calculations to create the treatment plan itself. However, with greaterprecision in the control of dose distribution comes increasing standards for the accuracy ofdose calculation. To reduce the occurrence of skin toxicity in patients, accurate prediction ofsurface dose is necessary. This includes the ability to simulate and reproduce the effects ofpossible perturbing factors, such as the presence of gaps between a bolus and the patient’sskin.To investigate the effects of these gaps on surface dose, and the effectiveness of MC and AAAcalculations in reproducing these effects, we have conducted a study inspired by the workof Khan[30] described in Chapter 1. Our “virtual” treatments are a computer reproduction71of this study, and we confirm the results of these simulations using ionization chamber andEBT3 film measurements.4.2 Measuring and Analysing Surface Dose EffectsFor constructing and running the simulations, the same process as described in Chapter 3.3was used. However, for this study the phantom files also included a 1cm thick bolus of waterthat was “floated” at set distances above the main body of the phantom. Otherwise, the beamenergy, field sizes, SSD and angle of incidence were the same as described for the validationstudy.The apparati used for ionization chamber and film measurements are shown in Figure 4.1.As with the computerized methods, the core elements of the arrangement are the same aswas used for measuring the PDD curves, described in Chapter 3. However, for the specificpurposes of this study, the only point of measurement was at the surface of the solid-waterphantom. A 30x30x1 cm3 slab of solid-water was introduced to serve as our bolus. Theslab was supported by four spacer posts with adjustable heights to create well-defined gapsbetween the bolus and the phantom. These posts were constructed from interlocking bricksmade from a thermoplastic material (acrylonitrile butadiene styrene) i.e. LEGOTM. To try toapproximate the gap sizes g used in the computer simulations, various combinations of threedifferent types of bricks were used:• A “standard” brick. Height = 1.149 cm.• A base brick. Height = 0.502 cm.• A flat brick, similar to the base bricks but with no ’bumps. Height = 0.313 cm.72(a) (b)(c)Figure 4.1: Experimental procedure for measurement of surface dose with increasing gapsize, using a Markus parallel plate chamber (a) and EBT3 film (b). c) A photographshowing the phantom and bolus assembled for use in Markus chamber experiments.73These brick heights reported above were measured using a micrometer screw gauge. Re-peated measurements of the same brick, and of different bricks of the same type, resultedin the same value. This would indicate that the statistical variance between these bricks issmaller than the precision of the micrometer± 0.001 cm. All support posts were constructedfrom these bricks in the same manner for a given height, yielding experimental gap values inthe range of 0.5 to 5.3 cm. The gap sizes were confirmed at each stage of the experiment bydirectly measuring the distance between the surface of the phantom and the bottom surfaceof the bolus slab, at the centre of all four sides of the phantom, using a micrometer. Wealso digitally measured the surface incline of the solid-water bolus with respect to phantomsurface and the treatment couch. The measured incline was consistently below 0.1◦. Basedon these results we, conservatively, estimate the uncertainty in gexp to be ≈ 0.005 cm.It is important to note that long strips of EBT3 films (2x20 cm2) were used for surface dosemeasurements, unlike the small pieces that were used to construct the PDD curves shown inthe preceding chapter. The long axis of these strips were oriented along the x-axis of thebeam, using the markings of the linac’s light field as a reference. Longer strips were usedso that lateral surface dose profiles could be obtained in addition to the surface dose at thecentre of the field. The effects of bolus-skin gaps upon these lateral profiles will be discussedfully in Chapter 5.In investigating the effects of bolus air gaps, the natural point of comparison is the surfacedose absorbed when a bolus is present and in full-contact with the patient. Therefore, weproceed with our analysis by determining the surface dose as a function of gap size, relativeto this reference condition, by defining the quantity ∆(g).∆(g) =Ds(g)Ds(g = 0)(4.1)74Where, Ds represents the dose at the phantom “surface”, collected along the central beamaxis. Of course, dose cannot practically be collected at the true surface (z=0). Therefore Ds,represents the dose at the shallowest possible measurement point for the given instrument.For MC phantoms this would be the centre of the first voxel (z = 0.0025 cm). This is thesame effective depth of measurement as the Markus chamber. For EBT3 films, the depth ofmeasurement is taken to be in the centre of the active layer at z=0.0189 cm. The quantity ∆can be described as representing the relative surface dose (in Gy), or a dimensionless DoseReduction Factor (DRF).As noted previously, parallel plate chambers are known to overestimate surface dose[25].However, the deviation between the chamber measurements and the true surface dose isexpected to be the equal for a given depth and a given chamber configuration, and is notinfluenced by the change in g. Therefore, any correction factor would be canceled out andwe may determine ∆ directly from the measurement of charge within the ionization chamber.∆(g) =Ds(g)Ds(g = 0)=Qs(g)Qs(g = 0)(4.2)An average of four measurements, two values each for both positive and negative chambervoltages, was taken for the final value of charge. The relative errors of these charge valueswere less than 0.3%, resulting in relative errors of ∆ of less than 0.1%.For EBT3 measurements, surface dose values were obtained from FilmQA Pro dose mapsin the same manner as the dose values used to create the PDD curves in Chapter 3. Similarprecautions regarding film orientation, scan direction and the avoidance of possible edgeeffects were followed. Each film strip was marked at its centre so that it could be alignedwith the central axis of the linac beam. Two 10 pixel by 10 pixel regions were selected aboveand below this mark. The average pixel value from both these regions was used to determine75Ds(g) with typical standard errors of less than 0.03 cGy. The resulting errors in the ratio ∆were between 0.004 and 0.006.A MATLAB script called “getDsurf.m” was used to extract surface doses from the MC andECLIPSETM dose matrices and is described in the appendix.4.3 Results and DiscussionIn Figure 4.2, the results of our MC simulations are shown. The effects that bolus-skingaps have on surface dose, as simulated in our models, are in general agreement with thoseobserved by Khan and by other researchers [13, 44]. As described in Chapter 1, the intro-duction of an air gap reduces the surface dose as compared to the case where the bolus is infull-contact with the phantom. The relative dose is further reduced as the distance betweenthe bolus and the phantom surface is increased. The scale of this decrease also dependson the field size, with larger fields demonstrating less loss in surface dose. Our MC resultsconfirm these observations.However, when compared to the results from Khan et.al our MC data shows greater dosereduction for similar gaps sizes using a given field. For example, for a 1 cm air gap and a10 cm2 field, MC determined DRF is ∆≈ 0.95, whereas, Khan’s measurement would suggest∆≈ 0.99. Similarly, Khan’s findings indicate that the dose reduction is almost negligible for15 cm2 fields, even with a 5 cm gap. However, our simulations show a pronounced decreasein relative dose at all gap sizes.76Figure 4.2: MC results showing effect of bolus-surface gaps (g) on surface dose. Doses aregiven normalised by the surface dose measured when no air gap is present (g = 0).Absolute errors in relative dose (∆) are two small to be shown and were less than 0.006for all field sizes. Bolus thickness was 1 cm.Different sensitivities to the “gap-effect” are also apparent when comparing results obtainedusing different measurements methods. Figure 4.3 compares results from MC, AAA,EBT3films and the Markus chamber from a 10x10 cm2 field. It is clear that both the EBT3 filmsand the Markus chamber show different levels of surface dose reduction for comparable fieldsizes. The Markus results are particularly interesting as the chamber previously demonstrated77excellent agreement with MC calculations for PDD, but here shows substantially higher valuesfor ∆(g).Figure 4.3: The effect of bolus-surface gaps on surface dose for a 10x10 cm2 field as mea-sured using MC, AAA, EBT3 films and a Markus parallel-plate ionization chamber. Bo-lus thickness = 1 cmThe varying sensitivities of the methods shown above can be elucidated by consideration ofFigure 4.4. This Figure shows MC derived PDD curves in the first 1.5 cm of the phantomfor gap sizes between 0 and 4 cm. It is apparent that large bolus-surface gaps result inthe reestablishment of a dose build-up region, in agreement with the findings of Sroka et.al78[44]. The return of a high dose gradient in the near-surface region also brings back theissues with measuring doses in these gradients. Although the Markus chamber has a pointof measurement comparable with that of MC, the chamber cavity is 2 mm thick, and so thedose is averaged over a large part of the new build-up region. The measured dose is stilllower than the value obtained when g = 0, however, but less than one might measure if thecharge could be collected over a smaller volume, therefore the Markus yields higher valuesof ∆(g). EBT3 has an active layer thickness of 28 µm, and so it has higher resolution thanthe Markus chamber. However, this active layer is at greater depth than the first voxel of theMC phantom and receives higher dose, therefore ∆(g) values obtained with EBT3 films arestill higher than comparable values from MC.79Figure 4.4: The effect of bolus-surface gap size on PDD (each curve is normalized to its ownmaximum dose), as shown for the first 5 cm. It can be seen that the presence of largegaps restores the build-up of dose near to the surface, in agreement with the results ofSroka et.al [44]. Bolus thickness = 1 cmThe reappearance of the build-up region confirms that the electronic equilibrium of the beamis significantly perturbed at large bolus-skin gaps. As discussed in Chapter 1, the dose ata given plane in the medium (transverse to the beam) is deposited by electrons that wereset into motion at shallower depths. The application of bolus takes advantage of this effectby providing additional material to generate enough electrons to deposit higher doses in thepatient’s skin. However, with significantly lower density, air is a poor material for generating80electrons. Therefore, presence of an air gap between the bolus and the skin results in fewerelectrons reaching the surface region and reduces the dose at the surface.Sroka et.al suggested that at large gaps sizes, such that zm is restored to its standard (withouta bolus) value, the influence of the bolus can be ignored. However, we do not believe thisto be entirely valid, as the electrons that are released from the bolus material will be presentwithin the beam and will deliver dose to the surface. This will result in higher PDD in thenear-surface region compared to values observed with no bolus present. Given the largeCSDA range of electrons in air (0.1995 g/cm2 [4] or≈163 cm), this influence will persist forlarge gaps. The scale of this range would also suggest that very few of these bolus electronswill be lost from the beam. However, they are highly likely to be scattered and travellingthrough the air gap at angles relative to the central beam axis. The distribution of surfacedose will, therefore, be spread over a wider area, which would have significant consequencesfor the accurate delivery of dose to a prescribed PTV. We will investigate this effect furtherin Chapter 5.The most interesting result apparent from Figure 4.4, is that AAA calculations do not demon-strate any reduction of surface dose due to the presence of even large bolus-surface gaps.For all gap sizes between 0 and 5 cm, values of ∆(g) calculated in ECLIPSETM remain ap-proximately constant. As AAA calculations were performed on virtual phantoms with 0.25cm3 voxels, it might be considered that the reduction of surface dose is simply averagedout in these larger voxels. However, the decrease in ∆(g) was observed in MC calculationsperformed at this voxel size. Therefore, we may conclude that the AAA algorithm does notaccount for changes in surface dose due to the presence of air gaps.This result is not unprecedented as AAA calculations have been shown to be inadequatein describing dose calculations involving extreme heterogeneities. The 2015 work of E.A.Alhakeem found that AAA calculations failed to model any change in the PDD curves due to81the presence of an air cavity in the build-down region [7]. The results of this article and ourown investigations seem to indicate that, although AAA can perform adequate calculationsfor anatomical inhomogeneities such as lungs [24, 42], it practically ignores extremely lowdensity interfaces such as air cavities of bolus-surface gaps.The AAA accounts for the presence of inhomogeneities by radiological scaling, i.e. thefunctions which describe the attenuation and scattering of photons and electrons are rescaledin each voxel i, and in all directions, by the relative electron density ρw [43, 46].ρw =ρeiρewater(4.3)The relative electron density for air is ≈ 0.001, which would lead to very severe reductionsto the energy-deposition functions and scattering kernels. One could speculate that in orderto avoid the need for such dramatic corrections, the program includes a threshold density forapplying the rescaling process. Media with densities as low as that of air could be assumedto have little practical effect on the distribution of dose, which is not unwarranted given howsurface specific the dose reduction appears to be, and so the program does not attempt therescaling. This could possibly explain why the AAA calculations do not appear to account forair gaps, either in our work or that of Alhakeem et.al, but does make some correction for lunginhomogeneities. Of course, the actual computer code that performs the AAA calculation isproprietary and so confirmation of this assumption would be difficult.In conclusion, our results indicate that the presence of air gaps between a bolus and the pa-tient’s skin will reduce the central surface dose relative to that measured when the bolus is infull contact. The presence of an air gap has been shown to disrupt the electronic equilibriumof the beam and reestablish the build-up of dose in the near-surface region. These findingsare in agreement with previous investigations on this subject. However, our investigations82also demonstrate that the AAA calculations do not appear to account for this effect, whichcould lead to inaccurate estimations of dose within patient treatment plans. Furthermore, ourdata shows that Monte Carlo simulations can model the effects of the bolus-surface gap andcan be used to produce accurate dose calculations in clinical contexts, and to form the basisof a “virtual laboratory” in the exploration of this phenomenon.83Chapter 5The Effects of Bolus-Skin Gaps onLateral Dose Profiles5.1 IntroductionThe results of the preceding chapter demonstrate that the presence of an air gap between abolus material and the patient can reduce the dose at the skin. It was also demonstrated thatthe AAA, a commercially available and widely-used dose calculation method, was unable toaccount for this effect. These findings have clear implications for treatment planning anddelivery in clinical scenarios, especially if the treatment requires significant dose to the skin.However, the magnitude of the dose is not the only parameter of key significance in treat-ment delivery. Radiotherapy methods, such as IMRT, sculpt and shape the three-dimensionaldistribution of dose with a high-degree of precision. For these techniques to operate success-fully the shape and spread of dose within the medium must be well-characterised. Therefore,the potential effects that a bolus-skin gap has on dose-distribution must also be understood.84In this Chapter, we will analyse the effects of increasing air gap sizes upon the lateral surfacedose profiles of a 6 MV treatment beam. Our analysis will concentrate on results obtainedfrom the same MC simulations that yielded the results described in Chapter 4. We validatethese findings using experimental data obtained from EBT3 film strips, which are well-suitedto this task as they allow the measurement of dose across a 2D plane.During the film experiments described in Chapter 4 (Figure 4.1b), long strips of EBT3 filmwere used so that line profiles along the X-axis of the beam could be also acquired. Profileswere obtained from the (FilmQA Pro) dose maps by isolating 10 pixel x 1000 pixel regionof interest, centred upon the midpoint of each film strip. The dose values were then averagedalong the short axis to create a single line profile.It is important that any factors specifically affecting the shape and spread of the surface dosedistribution are separated from the dose reduction effect observed in Chapter 4. To achievethis we have normalized each dose profile by its mean central dose. We refer to this relativedose value as Ξ(x,g), which is a function of position on the x-axis and gap size (g) as follows:Ξ(x,g) =D(x,g)D(x = 0,g)(5.1)For MC simulations, the value of D(x = 0,g) was determined as the average of the fourcentral surface voxels. Experimental Ξ profiles were measured using the same central dosevalues that were used for the calculation of the relative dose ∆ in the previous chapter.5.2 Results and DiscussionFigure 5.1 compares MC calculated relative surface dose profiles, for a 10x10 cm2 field andwith air gaps in the range of 0- 5 cm, with those obtained experimentally using EBT3 film fora similar range of gap values. In both data sets we can clearly observe that the presence of an85air gap significantly alters the shape of the dose profile. When the bolus is in contact with thesurface (g=0), the dose distribution closely matches the idealized “square” shape with littledose deposited outside the boundaries and approximately equal dose across the field’s span.As the distance between the bolus and the phantom is increased the profiles becomes more“rounded”. Dose near the inside edges of the field is reduced and there is a steady increasein dose outside of the field boundary for larger gap sizes.(a)86(b)Figure 5.1: Variation in the shape of the lateral surface dose distribution due to increasingbolus-surface distance. Each profile presents the dose relative to the mean dose at thecentre of the field (Ξ(x,g)). Data was derived from a) Monte Carlo and b) EBT3 filmmeasurements. Bolus thickness = 1 cm.The results from MC calculations show good agreement with the profiles obtained with filmmeasurements. Both data sets clearly show the degradation of the beam profile as the gap-size increases. This is further support for the validity of our MC models as providing accuratereconstructions of the gap effect.To quantify the spread of the beam profile we have measured the penumbra p(g) as a functionof the air gap size. The standard definition describes penumbra as the distance betweenthe 80% and 20% isodose levels. Here we use a slightly modified definition and use thedistance between the points of the profile where Ξ(x,g) are equal to 0.8 and 0.2. However,87the MC results have a lateral resolution of 0.25 cm, which makes direct comparison withexperimental values (resolution: 0.17 mm/pixel) more challenging.Previous work in the literature has modelled the sigmoidal shape of the treatment beam edgeusing the error function [34]. However, we have found a related expression, the Logisticfunction provides a higher quality fit to our data. We have, therefore, used a non-linear leastsquares method to fit our relative dose profiles with the function described in Equation 5.2.This resulted in high-quality fits (R2 values between 0.999-0.997) that were used to createapproximate beam profiles from which more precise beam penumbra could be estimated.Ξ(s) =A1+ e−k(s−s0)+ c (5.2)Figure 5.2: Monte Carlo calculated relative dose profiles for the edge of a 6 MV beam with10x10 cm2 field. The data points are fitted with the logistic function defined in Equation5.2 (solid lines). Bolus thickness = 1 cm88The variable s represents the position along the beam’s x axis, as measured from the fieldedge. The constants A, s0 and k correspond to the curve’s maximum value, midpoint andsteepness, respectively. The dose profiles were sampled so that the data was centred upon thepoint where Ξ(x,g)≈ 0.5), which, based on standard definitions, is the approximate locationof the beam edge as defined by the linac’s light field. The quantity c can be interpreted asthe minimum value of Ξ(x,g) within the range of voxels studied. This value corresponds tothe relative dose measured at the furthest point outside of the defined radiation field. Thesteepness parameter k provides a useful measure of the increasing spread of dose at largergap sizes, with lower values indicating a higher degree of scatter.The fitted coefficients for our MC data are shown below in Table 5.1. R2 values are alsoprovided as an indication of the quality of fit. Uncertainty was estimated by taking the RMSvalue of the 95% confidence bounds for each coefficient. The mean relative uncertainty inthese fitted parameters was approximately 4%, 20%, and 10% for A,c and k, respectively.It can clearly be observed that, for all three field sizes, the steepness parameter decreasesrapidly confirming the increased spread of dose at the phantom surface.5x5 cm2 10x10 cm2 15x15 cm2g A c k s0 R2 A c k s0 R2 A c k s0 R20 0.987 0.019 9.536 0.017 0.999 0.975 0.035 8.918 0.012 0.999 0.960 0.047 9.348 0.032 0.9990.5 0.967 0.031 3.548 0.006 0.999 0.929 0.047 3.409 -0.013 0.999 0.947 0.058 3.227 0.0042 0.9991.0 0.954 0.046 2.478 -0.015 0.999 0.929 0.058 2.168 0.015 0.999 0.893 0.072 2.226 0.003 0.9992.0 0.928 0.082 1.819 -0.061 0.999 0.870 0.097 1.578 0.013 0.998 0.844 0.104 1.505 -0.0017 0.9983.0 0.892 0.121 1.661 - 0.112 0.998 0.845 0.121 1.314 -0.013 0.998 0.879 0.108 1.058 0.080 0.9964.0 0.854 0.1661 1.630 -0.155 0.998 0.840 0.143 1.113 -0.004 0.997 0.764 0.149 1.139 -0.105 0.9975.0 0.8133 0.202 1.661 -0.129 0.995 0.790 0.177 1.156 -0.048 0.998 0.766 0.172 1.036 0.037 0.996Table 5.1: Coefficents obtained from fitting a Logistic function to the shape of lateral doseprofiles.The curves obtained from these logistic fits were then used to produce a more precise esti-mate of the dose penumbra in our MC results. Table 5.2 compares experimentally measuredpenumbra with those obtained from MC data using logistic curves.89MC fitted penumbra [cm] Experimental penumbra [cm]g 5x5 cm2 10x10 cm2 15x15 cm2 g 5x5 cm2 10x10 cm2 15x15 cm20.0 0.29 0.32 0.32 0.0 0.33 0.34 0.320.5 0.82 0.93 0.94 0.5 0.75 0.83 N/A1.0 1.21 1.44 1.51 1.2 1.27 1.52 1.522.0 1.75 2.24 2.53 2.4 1.96 2.64 2.893.0 2.12 2.86 3.35 3.4 N/A 3.18 N/A4.0 2.54 3.51 3.98 4.3 2.79 3.82 N/A5.0 3.50 4.00 4.44 5.3 3.05 4.22 N/ATable 5.2: Values showing the dependence of profile penumbra on the size of bolus-surfaceair gaps. Experimental values were obtained directly from EBT 3 measurements. Valueswere estimated from MC results using logistic regression.Both experimentally measured penumbra, and those determined from MC simulations, areshown to widen with increasing bolus-skin distance. The observed distortion of beam profileshas clear clinical implications, as dose is both reduced on the inside of the beam edge andincreased outside of the boundary. In the context of a treatment plan this would result inan underdosing of the target with higher doses delivered to at-risk structures adjacent to thePTV.However, the change in shape of the dose distribution was observed to be localised to thenear-surface region as shown in Figure 5.3 for a 10x10 cm2 field. Dose profiles taken atgreater depths exhibit a “square” shape and are a closer match to the surface dose measuredwhen the bolus is in direct contact with the phantom. Using Logistic regression, as describedabove, penumbra were determined from the MC dose matrices for increasing depth. Figure5.3b shows the estimated penumbra, for each gap size, relative to the value found in the caseof no air gap at the same depth. This penumbra decreases rapidly within the first millimetreof the phantom, and was found to reach unity within the first 7 mm of phantom depth. Thiswas observed for all three field sizes studied and demonstrates that the effect of the scatteredparticles becomes negligible within a short distance of the phantom surface.90(a)91(b)Figure 5.3: a) Lateral dose profiles for a 10x10 cm 2 at different depths. For comparison theblack line represents the relative dose at the surface for g =0. b) Decrease of fractionalpenumbra (ratio of measured penumbra to corresponding value at g = 0) with depth.Bolus thickness = 1 cmThe correlation between increased gap size and the observed widening of the penumbra, andthe surface specific nature of this effect, can be further understood by reference to the workof McKenna et.al regarding beam spoilers [34]. A beam spoiler is a layer of material, suchas polystyrene, that is placed in the path of the beam in between the linac aperture and thepatient. A “floating” bolus could therefore, be considered a beam spoiler. However, typicalspoilers are placed at a much greater distance from the patient than would be expected from92a clinically relevant air gap between the bolus and skin. In both cases, a large fraction of thedose deposited at the surface layer of the material originates from electrons generated withinthe bolus/spoiler. McKenna and her colleagues used MC to create a simulated spectrum ofthese electrons, which was used to determine the energy deposition kernels of these electronsand, hence, their effect on dose. Their results also show a significant increase in the beampenumbra when applying a spoiler, as our results do in the case of a large bolus air gap.When electrons are produced, via interaction with primary beam photons, in the bolus ma-terial they are incident upon the phantom surface with a narrow range of probable angles.The introduction of a gap between the bolus and the surface seems unlikely to significantlyaffect the probability distribution of these angles. However, increasing the distance betweenthe phantom surface and the bolus will results in greater divergence for a given angle ofincidence and, therefore, the electrons will be spread over a greater lateral distance. In thisscenario, electrons emanating from a region near the beam edge will have a greater likeli-hood of passing out of the beam’s defined field before reaching the surface. This will leadto a reduced number of electrons reaching the surface near the inside of the field boundary,and a greater number escaping to the outside edge. This produces the observed rounding ofthe dose profile at larger gap sizes. Another effect of greater beam divergence at large bolus-skin distances, would be to spread the incident electrons over a greater area. This wouldcontribute to decreased surface dose on the central beam axis, as we have observed and wasdiscussed in Chapter 4.In conclusion, both MC simulations and radiochromic film experiments indicate that the dis-tribution of surface dose would be substantially altered by the presence of an air gap, betweenthe bolus and the patient’s skin, during photon beam treatment. Our results show a pro-nounced decrease in dose near the inside boundary of the field, and a corresponding increasein dose outside of the field. This would suggest that the air gap effectively “spreads” out the93dose across the edges of the treatment field, which is likely due to increased scattering fromsecondary electrons originating within the bolus material. These findings have potentiallyimportant implications for clinical practise as this effect may lead to patient PTVs becomingunderdosed whilst overdosing adjacent critical organs that should be spared. A main focusof future work would be to study this effect on more realistic treatment plans to determine ifthe magnitude of any resulting under/overdosing would be significant in a clinical context.94Chapter 6Conclusions and Future Prospects6.1 ConclusionBolus is a well-established method for adjusting the distribution of dose, during proceduresusing Megavoltage treatment beams, so that a greater amount of energy is deposited in thenear-surface region. This technique has clear value for the treatment of tumours that arelocated closer to the skin, as are common in cancers of the head and neck. However, practicalconstraints such as the use of immobilization equipment and the natural contours of thehuman body can often prevent all parts of the bolus material being in complete contact withthe skin. The resulting gaps would be expected to have a small but notable effect on theintensity of dose at the patient’s skin. Given the rapid progress of radiotherapy, allowing thecontrol of dose distribution to increasing precision, these small perturbations could becomesignificant influences on patient treatment. Therefore, we have conducted this investigationto characterize the effects that bolus-skin gaps have upon surface dose distributions.Our primary tool for our research has been MC simulations, and we have supported andvalidated the results of these calculations using ionization chamber and radiochromic film95measurements. Our findings indicate that the intensity of the surface dose, on the beamscentral axis, decreases as the distance between the surface and the bolus is increased. Inaddition, we have also shown that the distribution of dose at the surface is altered by thepresence of an air gap. Regions near the interior edge of the treatment field received areduced dose, whilst additional dose was measured outside of the defined treatment area.The results were consistent with a “spreading” of those dose likely caused by the additionalscattering of electrons produced in the elevated bolus material.During our investigation we have deliberately extended the size of the bolus-skin gap toinvestigate the relationship between surface dose and gap size. In clinical practise, the sizeof any notable gap between the bolus and the patient’s skin would be highly unlikely toexceed 1 cm. At this scale, the reduction in relative surface dose is small, less than 10% for5x5 cm2 fields, and is likely to be smaller for realistic gaps sizes. The reduction in dose alsoappears to be limited to the near-surface region, and for the size of air gaps that might beconceivably encountered in clinical scenarios, the effect is negligible only a few millimetresfrom the surface. Therefore, in terms of dose to volume, the reduction in dose could beconsidered a minor effect.However, rapid progress in modern radiotherapy techniques demand increasing accuracy andcontrol over the magnitude and distribution of dose. In this sense our findings are relevant,particularly the observation of increased skin dose outside of the defined treatment field.In situations where the treatment plan has carefully sculpted the distribution of dose so asto avoid at-risk organs, the spread of dose beyond the planned beam edges is of clinicalsignificance. Therefore, we suggest several ways that the research described in this thesiscan be expanded upon.966.2 Suggested Future StudiesFor further investigations we would suggest addressing limitations of the current study andexpanding upon it’s findings. The research we have described in this thesis was intendedto be the initial phase of work, aimed at demonstrating the extent of an effect of bolus-skingaps on surface dose and identifying key areas for future study. As such, our simulationsand research have considered only simple beam geometries and square field sizes. An initialextension of this investigation would be to study the influence of beam angles and beamshape on the bolus-gap effect. Suggested simulated experiments would include:Influence of beam angles Several radiotherapy techniques, such as IMRT, make use of mul-tiple treatment beams incident at different angles relative to the patient. Therefore, theeffect of a bolus-surface gap at non-normal incidence is a clinically relevant question.MC simulations similar to those described in this thesis, could be performed over a widerange of angles of incidence. This investigation should include a treatment beam inci-dent at 180◦, i.e. a beam that would first pass through the phantom before irradiatingthe bolus slab. In the presence of a bolus-surface gap, such a treatment beam couldgenerate electrons that are backscattered from the bolus to deposit dose on the patient’sskin. The possibility of such an affect is worth investigation due to the common use ofparallel opposing beams in radiotherapy.Influence of non-square fields Our results demonstrate that the reduction in surface dose,caused by a bolus-surface gap, is increased for smaller field sizes. MC simulations oftreatment beams using rectangular and circular fields should be conducted to determineif the scale of this effect is consistent using different field shapes. The influence ofdifferent field shapes on the observed scattering of dose in the near-field region wouldalso be of interest.97Partially blocked beams As established in Chapter 5, the presence of an air gap betweenthe applied bolus and the phantom surface significantly perturbs the distribution of dosein the field-edge region. The proposed cause of this effect was additional scattering oflower energy electrons that are generated within the bolus material. Therefore, it is pos-sible that this effect could be exacerbated by the presence of additional contaminatingelectrons, such as those scattered from the beam collimators (in the case of a half-blocked beam) or the application of a beam wedge. Therefore, additional simulationshould be conducted to elucidate these effects.Dynamic Beam Shaping The results of our investigation indicate that the size of the treat-ment field, and additional scattering effects, influence the magnitude and distributionof surface dose in the presence of a bolus-surface air gap. However, techniques suchas VMAT do not utilize static fields but, rather, use continuously moving mutli-leaf col-limators to shape the dose during treatment. Therefore, the effects of bolus-air gapsshould be investigated under the clinically relevant conditions of dynamic beam shap-ing. One question that should be addressed through MC simulations is: Does the reduc-tion in surface dose, observed with small fields, persist if the beam profile is continu-ously adjusted, or is the effect “averaged out” during the treatment.Clinical Treatment Plans In the 2013 study by Khan, the authors investigated the effectsof bolus-surface gaps on surface dose deposited during IMRT treatment plans, whichplaced the work into more medically applicable context [30] . Similarly, further in-vestigations with MC simulations should be used to establish the clinical relevance ofthe skin-dose reduction. In particular, the increase in dose measured outside of thetreatment field should be investigated in treatment plans in which this additional scat-tering could potentially overdose nearby at-risk organs. One method for conductingsuch a study would be to introduce a bolus into virtual phantoms derived from patient98CT scans. However, a more direct approach would be to collect suitable examples ofpatient treatment plans where notable bolus air-gaps can be observed in the planningCTs. The size of the air gap could be established from the images in the ECLIPSETMtreatment plan.The use of bolus in radiotherapy has a long history, stretching back to the beginning of the20th century. However, despite the development of water-equivalent, synthetic media suchas SuperflabTM, the general principle of shifting the point of dose maximum by applying alayer of additional material has not changed. Radiotherapy has undergone rapid progress interms of accuracy and control over dose distribution, and the complexity of delivery methods.Therefore, reexamining time-tested techniques in context of modern methods is an importanttask. The work described in this thesis is intended to stimulate further study into the effectsof bolus in modern radiotherapy, particularly addressing the presence of air gaps between thebolus and patient’s skin. We have identified several lines of promising study to expand uponthe results described in this investigation by further exploring the effects of bolus-surfacegaps on surface dose, and placing the phenomenon in direct clinical context. We hope thatour work stimulates further research into bolus and it’s effects on the accurate control of dosedistributions in radiotherapy.99Bibliography[1] (2009). NIST attenuation coefficients. → pages 4[2] (2015). Model n23343 Markus R© Plane-Parallel ion chamber. → pages 51, 60, 62[3] (2016). Gafchromic dosimetry media, type EBT-3. → pages 26, 61[4] (2017). NIST ESTAR (Electron Stopping Power and Range Tables). → pages 81[5] Abdel-Rahman, W., Seuntjens, J. P., Verhaegen, F., Deblois, F., and Podgorsak, E. B.(2005). 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This is not an exhaustive listof all analysis performed in our investigation. However, most further processes utilize andbuild upon these core functions.A.1 getPDD.mThis script was utilized to extract, store and plot the calculated Percentage Depth Dose (PDD)profiles.The inputs to the script are:• The .3ddose files containing the calculated relative dose, and associated errors, in eachvoxel. This can be entered in the function call or by GUI.• The coordinates to define where on the surface the profiles is measured. The default isto measure the PDD along the central beam axis.The outputs are:105• The PDD profile and the associated absolute errors.• The maximum dose measured along the profile and it’s error.function [PDD,errPDD,Dmax,err_Dmax] =getPDD(DoseFileName,error,point);%GETPDD - Calculates/plots Percentage Depth Dose from a given3ddose file.%DoseFileName = input(’Insert filename string’)% If a dose matrix (present in workspace) is specified load dosefrom GUI% or filename string.if or(isempty(DoseFileName),ischar(DoseFileName))[dose,error,bounds] = read3ddose_Abs(DoseFileName);elsedose = DoseFileName; % Proceed if fed matrices in workspace.endnvox = size(dose) % Number of voxelsspc = 30.0/nvox(1); %Spacing of voxelsspc = round(spc*100)/100% Depth here refers to the depth of the air block above the phantom% surface i.e. the location of the phantom surface.%Find the voxel index of phantom surface.106if nvox(3) == 2*nvox(1) % This applies to phantoms with uniform0.25 cm3 voxels.depth = 30;depth_idx = round(depth/spc)z = bounds{3}elseif nvox(3) > 2*nvox(1) % This applies to those phantoms withhigh-resolutiondepth = 30; % voxels in the near surface region.%depth_idx = 41depth_idx = find([diff(bounds{3})<0.1],1)-1z = bounds{3};elsedepth_idx = nvox(3)-nvox(1); % This would apply to Eclipse dosematrices.depth = depth_idx*spcz = [0:spc:(nvox(3)-1)*spc];end% This if statement allowed for PDD curves to be taken off of thecentral% axis at a position defined by the input "point"if isempty(point)prof_loc = nvox./2; % Find the centre of the phantom.elseprof_loc = (point+15.0)./spc;end107XDP = dose(prof_loc(1):prof_loc(1)+1,prof_loc(2):prof_loc(2)+1,:);% Take 4x4 cross-sectional profile through phantomDDP = squeeze(mean(mean(XDP,1),2)); % Average into single profile.DDP = medfilt1(DDP);[Dmax,idx] = max(DDP(depth_idx+1:nvox(3))) % Find maximum dose &depth-index of voxeldmax = z(depth_idx+idx)% Determine depth of maximum dosedisp(’Double-check this with data-browser!!!’)%Convert to percentage depth dosePDD = (DDP./Dmax);PDD = PDD*100;if ˜(isempty(error))XEP = error(prof_loc(1):prof_loc(1)+1,prof_loc(2):prof_loc(2)+1,:);XEP = (XEP.*XDP).ˆ2;XEP = squeeze((sqrt(sum(sum(XEP,1),2)))/4); % Error in averagedprofileXEP = (XEP./DDP); %Relative errorerr_Dmax = XEP(idx); % Error in DmaxerrPDD = (sqrt((XEP.ˆ2) + err_Dmaxˆ2));%Relative error in PDD;errPDD = (errPDD.*PDD); %Absolute error in PDDfigure()errorbar(z(depth_idx+1:end),PDD(depth_idx+1:end),errPDD(depth_idx+1:end))errPDD = errPDD(depth_idx+1:end);else108figure()plot(z(depth_idx+1:end),PDD(depth_idx+1:end))%plot(z((nvox(3)/2)-2:end),PDD((nvox(3)/2)-2:end))endPDD = PDD(depth_idx+1:end);title(’Central Percentage Depth dose profile’)xlabel(’Z (cm)’)ylabel (’Relative Dose (%)’)A.2 getDsurf.mThis script is a compliment to getPDD and determines the calculate surface dose along thecentral beam axis from a .3ddose file.The inputs include:• The 3ddose files containing MC doses and/or it’s errors, which can be chosen using aGUI.The outputs are:• The magnitude of dose, along the central beam axis, at the surface of the phantom, andit’s estimated error.function [Dsurf, DSerr] = getDsurf(DoseFileName,error);%Alows you to run with either a preloaded dose matrix, a typed indose file109%name or a GUI browser.if or(isempty(DoseFileName),ischar(DoseFileName))[dose,error,bounds] = read3ddose_Abs(DoseFileName);elsedose = DoseFileName; % Proceed if fed matrices in workspace.endnvox = size(dose)% These lines allow for different phantom types to be accounted forif nvox(3) >= 2*nvox(1)depth = 30;%depth_idx = 41depth_idx = find([diff(bounds{3})<0.1],1)-1z = bounds{3};elsedepth_idx = nvox(3)-nvox(1);%spc =%depth = depth_idx*spc%z = [0:spc:(nvox(3)-1)*spc];end%Find the voxel index of phantom surface.mid = nvox(1)/2;%Get dose and error from 4 central surface voxels.110Dsurf = dose(mid-1:mid+2,mid-1:mid+2, depth_idx+1);if ˜(isempty(error))DSerr = error(mid-1:mid+2,mid-1:mid+2, depth_idx+1);DSerr = DSerr.*Dsurf; % Convert to absolute voxel error.%Get absolute error in Surface Dose (using quadrature formula)DSerr = sqrt(sum(DSerr(:).ˆ2))/16endDsurf = mean(mean(Dsurf,1),2) % Mean Surface doseA.3 Yprofs.mThis code was used to measure and plot lateral dose profiles from the results of MC calcula-tions. The scripts determines and plots lateral dose profiles at depths of 0.5 cm, 1.5 cm, 3.0cm, and 6 cm, from the phantom surface.The inputs to the function are:• A string containing the name of a 3ddose file, or one can be selected from a GUIinterface.The outputs are:• A matrix containing lateral dose profiles at each of the specified depths.[dose,error,bounds] = read3ddose_Abs(DoseFileName);elsedose = DoseFileName; % Proceed if fed matrices in workspace.end111nvox = size(dose);spc = 30.0/nvox(1);spc = round(spc*100)/100 ;mid = nvox(2)/2;if nvox(3) >= 2*nvox(1)depth = 30;%depth_idx = 41depth_idx = find([diff(bounds{3})<0.1],1);prof_d = [0, 10 ,30, 60 ,120] + depth_idx;y = bounds{2};elsedepth_idx = nvox(3)-nvox(1)+1;prof_d = [0, 3, 4, 200] + depth_idx;depth = depth_idx*spcy = [-15.0:spc:14.75]+spc/2;endl = dose(mid:mid+1,:,prof_d);line_av = mean(squeeze(l),1) ;Y_sects = squeeze(line_av);centre_av = mean(Y_sects(mid-1:mid+2,:),1);Y_sects = bsxfun(@rdivide,Y_sects,centre_av);Y_sects = medfilt1(Y_sects);end112

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